Spallation yields of neutrons produced in thick lead/bismuth targets by protons at incident energies between 300 and 590 MeV

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FINAL VERSION: 23.12.02

Spallation yields of neutrons produced in thick lead/bismuth targets

by protons at incident energies between 300 and 590 MeV


K. van der Meer

a
, M.B. Goldberg
b
, E.H. Lehmann

c
,

H. Aït Abderrahim
a
, D. Bar

b
,

D. Berkovi
ts

b
,

M. Daum

c
,

S. Dekelver

a
, Y. Foucher

c
, J. Gerber
d
, F. Van Gestel

a
,

W. Hajdas

c
,

H
-
P. Linder

c
,

E. Malambu

a
, I. Mardor

b
, J. Oeyen

a
, D. Saphier

b
, A. Shor

b
, M. Willekens

a

and Y. Yariv
b


a

SCK●CEN, Boeretang 200, B
-
2400 Mol, Belgium

b

Soreq NRC, Yavne 81800, Israel

c

Paul
-
Scherrer
-
Institut, CH
-
5232 Villigen
-
PSI, Switzerland

d

IReS, F
-
67037 Strasbourg, France

PACS Codes:

25.40.Sc Spallation reactions

& keywords

27.80.+w

Properties o
f specific nuclei listed by mass range 190 <=A <= 219

28.20.
-
v Neutron physics

Abstract


Spallation
-
neutron

yields

for

protons

at

E
p

=

300,

420

&

590

MeV

incident

on

thick

Pb/Bi

targets

have

been

measured via

activation

analysis

of Au

& Mn foils

at

the

PSI

Proton Irradiation Facility. The data were obtained with the water
-
bath
method, in a novel variant that incorporates a detailed MCNPX simulation in the analysis procedure. The
y
include

slow
-
neutron

fluence

distributions

at all three proton energies,

Cd
-
ratio

distributions

at

E
p

=

300

MeV

and

total

n/p

values

of

6.0

±

0.3

&

9.6

±

0.4 at

420

&

590

MeV,

respectively.

The

latter are in line with neutron
-
yield systematics
for protons on thick Pb
-
targets, which are found to vary with remarkable regula
rity over a broad range of incident

energies.

The

results

of

the

present

work
,
along

with

those

obtained

recently

by

various

groups

on

thin

and

thick
-
target
neutron spectra,

neutron
-
multiplicities and the radio
-
nuclide inventory produced, constitute a data
base pertinent to the
design and optimization of new, high
-
intensity spallation
-
neutron sources at these proton energies.

1. Introduction


The last decade has witnessed a number of new, frontline initiatives in accelerator
-
based neutron sources. The goal

of

these

well
-
publicized

national

and

international R&D programmes is to produce high
-
intensity slow
-
neutron beams
via proton
-
induced spallation reactions [1,2]. Noteworthy among these are the proposed ESS


European Spallation

Source [3],

SNS



National

Spallation

Neutron

Source [4] under construction

at

ORNL

&

NSP



Neutron

Science
Project in Japan [5]. Prominent among already
-
existing facilities are the continuous source SINQ at PSI [6] and the
pulsed sources MLNSC at LANL, IPNS at ANL, ISIS at RAL
& COSY at Jülich.


Other related projects under consideration in this context are the so
-
called Accelerator Driven Systems


ADS [7
-
11].
These are envisaged to operate in conjunction with sub
-
critical assemblies in nuclear fuel cycle applications, such a
s
waste
-
transmutation

[7,10
-
15]

and

energy
-
production

based

on

the

232
Th



233
U

cycle

[16
-
18]. Lower
-
beam
-
energy
versions are also currently being considered [19] and designed (e.g., the

MYRRHA

project [20]), among others, to
replace research

reactors

i
n

radiation
-
damage/corrosion

studies

of

fissile

fuel

elements
.


With

regard

to the nuclear physics properties underlying these projects, proton
-
induced spallation reactions on various
high
-
Z

targets

at

incident

energies E
p

>

800

MeV have been extensively s
tudied, with respect to: neutron yields [21
-
28],
neutron

spectra

[29
-
35],

neutron

multiplicities

[36
-
40]

and

the

inventory

of

radio
-
nuclides

produced

[41
-
47]
*
.

However,
at

lower

incident

energies

the

experimental

data

on

such reactions is still rather sp
arse (see, e.g., [48]) and inadequate
for

reliable

and

accurate

predictions

on

neutron

yields

of

existing

and

planned

spallation

sources

in

the

E
p
=300

800

MeV
energy range. An up
-
to
-
date

status

review

of

the

data

at

these

intermediate

bombarding

energie
s

is

presented below.


The first systematic measurements of neutron yield per primary nuclear interaction in high
-
Z materials at proton
energies E
p
=300

800 MeV were performed at Chalk River using cosmic rays in 1960 [22], but the overall accuracy
of the
data

is low. Typical errors per point in these measurements were quoted as ~15% and the effect of secondary
interactions was estimated to be ~20% for the thinnest targets used (22

g/cm
2
).


Between 1968 & 1983, thick
-
target
yields for Pb targets of vario
us diameters immersed in a water bath were measured at proton energies E
p
=100

MeV
[26], 400, 500 & 660

MeV

[24] and in air at E
p
=250

MeV [27]. Similar experiments at energies up to

E
p
~1.2

GeV

using
polythene moderators had earlier been reported by the Ch
alk River [23] and Harwell [25] groups.

_____________

*

In this context, the elegant mass
-
spectrometry work by the GSI/Saclay/Orsay group [47] is especially noteworthy.


2

Measurements of the double
-
differential cross
-
section (with respect to neutron energ
y and emission angle) were first
performed on a broad range of thin targets at E
p
=585 MeV by a FZK
-
Karlsruhe/FZJ
-
Jülich group [29] in 1987 and
later extended for Pb
-
targets to higher proton energies at SATURNE [34] and to thick targets at KEK [35]. Neu
tron
multiplicity measurements on thick Pb
-
targets at E
p
=197 MeV [39] and for thin as well as thick targets throughout the
range E
p
=0.2

5 GeV were recently reported by a GANIL/HMI/Jülich collaboration [36
-
40].


The

above

essentially

summarizes

data

acquir
ed

on

thin

and

thick

high
-
Z

targets

to

date.


In

fact,

relatively

few thick
-
target

neutron
-
yield

measurements

have

been

performed

on

materials

other

than

Pb

in the

300

600

MeV range
[23,28,36
-
38,40
].
It

was

thus

decided

to

measure

slow
-
neutron

fluence

distributions

and

total

neutron

yields on thick,
high
-
Z targets using a water bath [26,49] at a number of incident proton energies in this range.


A second pertinent

context

relates

to

the

theoretical

basis

for

the

spallation

reaction

mechanism.

Since

th
e

fully
-
relativistic
,
quantum
-
mechanical

many
-
body

problem

is

inherently

very

complex
,
a

need

arose

for

tractable

models

that,
with suitable

approximations, would describe

the

conventional, non
-
exotic

features of the nuclear processes. The
most common o
f these is the Intra
-
Nuclear
-
Cascade (INC) [50
-
53] + Evaporation [54] model. However, at low
incident proton energies (E
p

<

~200

MeV) and to a lesser extent at higher energies (in collisions where most of the
projectile energy is dissipated in the prima
ry spallation event), the fundamental premise that the de
-
Broglie
wavelength of the projectile is short compared to typical inter
-
nucleon distances within the nucleus, is not fulfilled. In
other words, the approximation underlying the INC
-
model


that the incident proton, in its primary interaction with a
target nucleus, successively and independently collides with individual nucleons



is poor. As a result, spallation
simulation codes

[55
-
61] based thereon

are

inherently

outside their

validit
y range. Nevertheless, they still

work

surprisingly well

even at

low incident

energies,

accounting

for

many empirical features

of the

spallation

process.
Thus, considerable

effort has recently been invested in attempts to gain confidence in their applic
ability at lower
incident energies by appropriate ‘benchmarking‘ with reliable data.

Since

the

outputs

of

these

codes

serve

as

key

tools

in

designing

new

spallation

neutron

sources,

benchmarking

and

code

intercomparisons

[62
-
66]

are

desirable.


Another

re
levant

context

concerns

the

choice

of

target

material

in

a

spallation
-
neutron

source,

which

is

dictated

not

only
by neutron yield, but also by issues such

as: radiation
-
damage
-
induced

aging,

radio
-
toxicity

of

reaction

products

and

heat

removal

problems.


These are generally more severe than in nuclear reactors, in the sense that, typically, 1

MW
of

beam

power

is

dissipated

within

the

rather

small

volume

(relative

to

fissile
-
fuel

core

dimensions)

defined

by

the

beam
spot
-
size

and

range.


An

attractive

can
didate

in

this

respect

is

the

eutectic

alloy

LBE

(45%

Pb


55%

Bi)

that,

in

addition
to

producing

high

neutron

yields

and

having

low

cross
-
sections

for

re
-
absorption

of

thermalized

neutrons,

is

a

very

good,

albeit corrosive,

coolant

[67].

It

has

a

meltin
g

point

of

123
o
C

and

exhibits

favourable

heat

transfer

properties

[67,68].


Based on the above considerations it is obvious why several large
-
scale spallation
-
neutron
-
source programs have
designated

LBE

as

the

target

and

coolant

of

choice. The

MEGAPIE

co
llaboration [69] is studying and evaluating the
applicability of LBE as a spallation target and primary target coolant at 1

MW beam power. The thermo
-
hydraulics
studies and others undertaken within MEGAPIE will have implications for SINQ at PSI [6], MYRR
HA at Mol [20] and
other CW spallation neutron sources currently under consideration
**
.


A further key issue addressed by MEGAPIE refers to radio
-
toxic reaction products generated in target materials under

consideration

and

the

associated

environmental

safety

implications.

Prominent

among

these

is

the

inventory of
polonium isotopes (particularly the

-
emitters
210
Po and to a lesser extent,
208
Po &
209
Po) produced in Bi, the majority
component of LBE. The data on yields of
202



210
Po in Bi targets bombarded by protons at intermediate energies is
still relatively sparse [46,71
-
75], but yield values

can readily be obtained by activation

analysis

with gamma
-
ray

and


-
particle

spectroscopy.

Within

the

present

project framework,

it

was

decided

to

address

this

problem

too. Thus, the

appropriate

irradiations were performed and the data are being anal
ysed.


In summary, design/optimization of intermediate
-
E
p

spallation sources requires achieving the following goals:


1.

to measure integral neutron/proton yields on water
-

surrounded Pb/Bi targets at intermediate

E
p


2.

to study the spatial distributions of slo
w neutrons in the moderator around the extended radiation source


3.

to

benchmark

and

inter
-
compare

existing

transport

codes

at

low
-
E
p

,

where

their

validity

is

in

question


4.

to determine the inventory of radiotoxic isotopes for Pb/Bi targets in low
-
E
p

proton
-
induced spallation reactions


The present work primarily addresses objectives 1

& 2. The latter will be the subject of a separate publication.

_____________


**

For

pulsed thermal

and

‘cold‘

neutron

sources,

preserving

the

pulse

time
-
structure

is

a

cri
tical

consideration.

The

latter

depends

strongly

on

the

neutron
-
absorbing/moderating

properties

of

the

target. In

this

sense,

metals such as

W, Ta
& Hg [70] are considered more favourable than LBE.


However, beam
-
power dissipation at new

large
-
scale
facilities
(up to ~5

MW) [3
-
5] could clearly pose target
-
stability problems with solid or volatile materials.


3

2. Experimental

In order to fulfil the above
-
mentioned objectives, the integral thick
-
target fast
-
neutron yield per proton
n/p

and spatial
dis
tributions of thermalized neutrons were determined using the water
-
bath/activation
-
foil method [49]. The basic
premises of conventional variants of this method are:

a)


the primary neutrons from the radiation source are predominantly contained within the w
ater

moderator

volume


b)


it

is

possible

to integrate

the

measured

thermal

fluence

distribution

over

the

water

volume

with

adequate

precision

It is noteworthy that fulfilling (b) in the case of spallation reactions at these energies would have necessitated t
he use
of an extensive, finely
-
spaced grid of activation foils. This is due

to

the extended

radiation

source

and highly

anisotropic

component of the fast
-
neutron

fluence

distribution characteristic of such reactions.

In

the

present work a

different appro
ach, representing a novel variant of the water bath method, was

adopted: the
fluence integration was circumvented by relating a restricted set of sampled foil
-
activities to the integral quantity
n/p

via

a

detailed

simulation

of

the

entire

process

using

the

MCNPX

code

[60].

This procedure has fundamental
implications for the experimental setup, data analysis and associated code
-
verification issues.


2.1
Experimental setup

In the experiments, the target was surrounded by a water bath of dimensions app
roaching 1

m
3
. Slow
-
neutron
fluence distributions were determined by means of thin Au (with and without Cd cover) and Mn activation foils, placed

at well
-
defined

axial and

radial

positions

within

the

water

bath.

Via their n
slow

capture cross
-
sections,

these materials
and configurations exhibit differing sensitivities to the thermal and epithermal neutron distributions [76]. Following
irradiation, the absolute foil activities were determined with an efficiency
-
calibrated, shielded Ge detector.


A sch
ematic view of the overall experimental setup is shown in Fig. 1. The Proton Irradiation Facility in the NA
-
2
target hall (now dismantled) at PSI´s 590 MeV high
-
current proton cyclotron facility was located at the end of a beam
distribution system compris
ing an electrostatic beam splitter, beam
-
energy
-
degraders, analyzing magnets, beam
-
line
optics and diagnostics modules, that combined to provide good
-
quality, energy
-
variable beams of nA intensity for a
variety of nuclear physics studies and other applicat
ions [77,78].





Fig. 1 Schematic view of experimental setup in NA
-
2 target hall
.



As seen in Fig. 1, the

experimental

assembly, comprising a Pb/Bi target enclosed within a water bath, was located at
the end of the PIF beam

line, inside a ~1

m thi
ck concrete enclosure. Along this beam line were two quadrupole
lenses and

a

set

of x,y magnetic

steerers. At

the

end

of

the

vacuum

tube

the

beam

emerged

into

air

through

a

thin Al
window located ~1

m upstream from the target.


4

A

scaled

drawing

of t
he

plexiglass

water bath

assembly is

shown

in Fig. 2.


It is similar to that described in ref. 26, the
dimensions

being 1000

mm

(L)

x

750

mm

(W)

x

900

mm

(H). A hollow, water
-
tight, plexiglass shaft is inserted into the
water bath to house the target.

Thus, the proton beam strikes the target directly through air.

A bath of this size
effectively contains most of the neutrons emitted from the target. In fact, such containment is
not inherently required

in the new variant of the method employed here
, but was dictated by local radiation safety requirements.



Fig. 2


Drawing of water bath assembly and principal components (all dimensions are in mm). The
latter primarily comprise the target shaft/assembly and the neutron activation foil holders
.




2.2
Target & activation foil assemblies

As mentioned in the Introduction,

Pb/Bi

was used as target material, since its 45%
-
55% eutectic alloy LBE [67] has a
low melting point (123°C) and is a promising candidate for high
-
power, high
-
neutron
-
flux liqui
d
-
metal spallation
sources [68]. The target was cylindrical, its configuration being broadly representative of a typical high
-
intensity
spallation source. However, for the sake of simplicity and to enable beam
-
energy
-
differential activation analysis
studi
es of spallation products on Pb and Bi separately, the target was designed as a modular sequence of alternate
Pb and Bi disks, each 10 mm thick and 100 mm in diameter.

For the irradiations at 300, 420 & 590 MeV proton energy, a total of 16, 18 & 30 disks w
ere respectively used, the
corresponding proton ranges being ~95 mm, ~160 mm & ~275 mm [79]. Schematic

views

of

the

target

assembly
and the activation foils within the water bath

are

shown

in

Figs.

3 & 4.



Fig. 3


Schematic view of target with Al ac
tivation foil and alternate Pb (dark), Bi (light) disks. The axial
distances
Z


of the neutron activation foils from the target are measured along the beam direction,
from the point where the protons impinge on the first Pb disk
.


5

To

sample

the

spatial

distributions of thermal

and epithermal neutron fluences in the water, a number of plexiglass
guide
-
tubes, inserted at several locations perpendicular to the central target shaft, held Au and Mn activation foils
within the water, at

well
-
defined

axial

(
Z



c
.
f
.
Fig
.
3)

and

radial

(
R



c
.
f
.
Fig
.
4)

positions

relative

to

the

target.


The guide
-
tubes were mounted on the radial extensions of the 3
rd

(Pb), 6
th

(Bi), 9
th

(Pb), 13
th

(Pb) and 16
th

(Bi)
disks, in the plane of the axial centre of each (10

mm th
ick) disk. Thus, the axial coordinates of the foils were
Z

= 25,
55, 85, 125 & 155 mm, respectively. The radial coordinates of the foils were
R

= 76, 126, 176 & 226 mm.
Consequently, neutrons created at the centre of the target and emitted radiall
y outward (at 90
o

to the beam direction),
will traverse projected distances of 50 mm (the target disk radius) of lead or bismuth, plus 26, 76, 126 and

176 mm of
moderator (water

&

plexiglass),

on

their

trajectory

towards

activation

foils

located

at

the

rad
ial

distances

R
, as

shown

in

Fig.

4.


Fig. 4 To
-
scale drawing of target disk and an adjacent plexiglass guide tube with 4 activation foils, looking
along

the

proton

beam.

Radial

distances
R

[in

mm]

of

foils

from

the

target

central

axis

are

shown

on

lef
t
.



In the 590

MeV run, the target length was extended, in order to account for the higher proton range. Accordingly,
additional

Au,

Mn

activation foils were placed at radial distances
R

= 76

mm, adjacent to disk Nos. 18, 21, 24, 27 &
30 (at axial coord
inates
Z

= 175, 205, 235, 265 & 295

mm, respectively).


6

3. Data Analysis and Results

This Chapter describes the experiments, computer
-
simulations and analysis procedures put into practice in order to
determine the slow
-
neutron
-
fluence distributions in t
he water moderator surrounding the target, as well as values of
n/p
meas
, the total number of neutrons emitted per proton from the thick

Pb/Bi

target at several bombarding energies.
In this context, it should be noted that the latter is determined as a r
atio of two independent, absolute quantities.

As

such,

no cancellation

of

errors,

be

they

of

statistical

or

systematic

origin,

occurs

in

the

process.


3.1
Determining the number of protons per irradiation

At each bombarding energy, the incident beam
was centred on the target and aligned along its axis to

within

~2

mm
and

~1°,

respectively, with the aid of a

beam

profile

monitor

and

imaging

plates.

Typical

transverse

beam

dimensions
were ~20

mm diameter FWHM.


Deviations of the beam spot shape from p
erfect circularity were no more than ~5%
at 300, 590

MeV and ~20% at 420

MeV.



In

determining N
p
tot
, the

total number of protons impinging on target per irradiation, a principal problem arises from the

fact

that

the

intensity

of

nA

beams

at

these

en
ergies

cannot

be

accurately

measured

directly. The

total

number

of
protons per irradiation
was thus determined by activation analysis via the yield of a reaction with a well known cross
-
section.

To

this

end, a

high
-
purity, 0.28

mm thick Al
-
foil

with

th
e

same

diameter

as

the

target

disks

(100

mm) was
placed immediately in front of the first (Pb) disk (see Fig. 3). The activation reaction is
27
Al(p,3n3p)
22
Na. This
cross
-
section has been measured by numerous groups over the years and its dependence o
n bombarding
-
energy is
consistently found to be rather weak for 200

MeV

<

E
p

<

800

MeV [see, e.g., 43, 80
-
87]. The values, ranging from
~14 mb to ~16 mb, are quoted with varying accuracy (typically between 4% and 10% per

experimental

point), but are
f
airly consistent within

errors.

Averaging them,

we

adopt

the

following cross
-
section values

and

uncertainties:





= 14.6


0.6 mb at 300

MeV


= 14.8


0.6 mb at 420

MeV ,


= 14.9


0.6 mb at 590

MeV



The abso
lute
22
Na activities produced in this reaction were determined from the 1274

keV gamma
-
ray intensities using
a shielded, efficiency
-
calibrated, high
-
purity Ge
-
detector. These measurements were repeated a number of times
over a period of 1 year after irrad
iation, yielding mutually consistent results. Evidently, no activity is lost by
diffusion

of
22
Na ions out of the Al foil over such time intervals.



In contrast, corrections for activity losses due to
prompt recoil

out of the Al
-
foil (in both forward &

backward directions)
do need to be applied. This was done on the basis of empirically
-
studied recoil kinematics for

24
Na

produced in the
p +
27
Al reaction and

similar

reactions

over

a

broad

range

of

bombarding

energies

[88,89].


Generally, these

correc
tion

factors

are

found

to

be

small

and

almost

independent

of

beam
-
energy


.

The recoil kinematics for
22
Na necessarily
resembles that for
24
Na, since the randomly
-
oriented emission of two additional neutrons does not have a large effect
on the centre
-
o
f
-
mass motion. Invoking this similarity, the activity
-
loss estimates for
22
Na range from ~0.4% [88] to
~1.5% [89] for the Al
-
foil

thickness

in

question. A correction factor of 1% was thus adopted.



At the higher bombarding energies this procedu
re yielded for the total number of protons per irradiation:



N
p
tot

= (3.8



0.2)

x
10
13

at 420

MeV

N
p
tot

= (7.1



0.3)

x
10
13

at 590

MeV



the

errors

quoted stemming

predominantly from the adopted uncertainty (~4%) on the
22
Na production

cross
-
section.



For technical reasons,

this procedure

could

not be

implemented for the 300

MeV data, which remain unnormalized at
present. However, it is conceivable that when the quantitative analysis of the radio
-
nuclide inventory produced in the
ta
rget disks is eventually completed (see Introduction), it may yet prove possible to derive an experimental value for
N
p
tot

at 300

MeV, via some known production cross
-
section.





Table 1 summarizes the relevant irradiation parameters in the individua
l runs, along with the combinations of Au and
Mn activation foils (see

sect. 3.2 )

employed

to

determine

the

slow
-
neutron

fluence

distributions.



_____________



These findings reflect the feature that in such reactions, most of the projectile momentum
is imparted to the directly
-
ejected, forward
-
going nucleons at the
intra
-
nuclear cascade
(INC) stage [50
-
53]. Thus, the subsequently
-
emitted low
-
energy
evaporation nucleons

[54] as well as the
residual heavy fragment

acquire proportionately less momentum a
nd
the range of the latter in the target is correspondingly short.


7


Table 1: Overview of Irradiation Parameters & Neutron
-
Activation Foil Combinations



Run


E
p

[MeV]

Irradiation


Time [hrs]


N
p
tot

[10
13
]


Cd cover on Au


Activation Foils



Mn Foils


Employed


# 1


300



~

8.0


~ 10



@ several locations


no


# 2


300



~

5.5


~ 6



@ complementary locations to
# 1


no


# 3


420







10.67


3.8



0.2


no


yes


# 4


590





6.68


7.1



0.3


no


yes





crude estimate (to within ~30%) from prior experience in NA
-
2 hall




not accurate enough for normalization purposes


3.2
Procedure for deriving foil activities

The foil activities were determined by me
asuring the peak intensities of the 412 keV line from
198
Au and the 847 keV
line from
56
Mn, using an efficiency
-
calibrated, shielded intrinsic Ge detector. All activities have been corrected for
losses during and after irradiation, using the following hal
flife values:








T
1/2
(
198
Au) = 2.69157


0.00021 d


[90]







T
1/2
(
56
Mn) = 2.5785


0.0002 h


[91]



In order to apply the correction for decay losses during irradiation, which is particularly important in the
56
Mn case
where the halflife

is shorter than the irradiation time, it is necessary to know the detailed history of beam intensity on
target as function of time. For this purpose, a small array of gas ionization counters wired in parallel was placed in the
proton beam just in front o
f the water bath. The proton
-
induced current pulse from the counters was integrated in one
-
second time
-
intervals, then digitized and recorded as a histogram throughout each irradiation.



The measured activities have also been corrected for gamma self
-
ab
sorption (0.4%

&

0.2%

for

Au

&

Mn, respectively),
for extended gamma source geometry (1% in both cases) and for neutron self
-
shielding effects (estimated as 5.8% for
198
Au & 4.0% for
56
Mn) using values from ref. 76. Due to the close proximity of the Au
& Mn foils at each location in
the 420 & 590 MeV runs, corrections should, in principle, also be applied for neutron mutual
-
shielding. However,
these are clearly 2
nd

order effects compared to the self
-
shielding and have therefore been

neglected.


Typical

counting

statistics

errors

per

data

point

are 1

1.5% .


3.3
Measured specific
-
activity distributions

Tables 2
-
4 present the Au and Mn foil activity data for the irradiations at all three bombarding energies. Au
-
foil data
(without Cd cover) were taken at all 3 bombarding energies, whereas Cd
-
cover
ed Au
-
foil data were only taken at 300
MeV and Mn
-
foil data only at 420 & 590 MeV.



In the two 300 MeV runs (see Table 1) the Au foils were activated with or without Cd cover at complementary
locations (
R
i
,

Z
i
). The results of both 300 MeV runs for the

two foil configurations were cross
-
normalized via the
measured activity at the point (
R
=126,
Z
=25) and are presented in Tables 2a and 2b . Tables 3a & 4a show the
measured specific activities of
198
Au for Au foils without Cd cover at 420 & 590

MeV, res
pectively. Tables 3b & 4b
show the measured specific activities of
56
Mn for Mn foils without Cd cover

at

420 & 590

MeV,

respectively.


Table

2a:

Measured

198
Au

activities

without

Cd

cover

as

function

of

radial

(
R
)

and

axial

(
Z
)

foil

coordinates


at E
p
=30
0

MeV. The data, in units of
kBq/g
, were cross
-
normalized from Runs 1 & 2



Z

[mm]





R

[mm]




25


55


85


125


155


76


965

15


1010

15


860

15


705

10


527

8


126


488

7



500

8


451

7


355

6


257

4


176


178

3


181

3


162

3


134

2


101

2



226




55

1




57

1







37

1


8


Table 2b: Measured
198
Au activities
with

Cd cover as function of radial (
R
)

and axial (
Z
) foil coordinates


at E
p
=300

MeV. The data, in units of
kBq/g
, were cross
-
normalized from Runs 1 & 2

.


Z

[mm]






R

[mm]




25


55


85


125


155


76


197

3


196

3


181

3


128

2


81

1


126




75

1




48

1




176


19.4

0.3


19.9

0.3










Table

3a:

Measured

198
Au

activities

without

Cd

cover

as

function

of

radial

(
R
)

and

axial

(
Z
)

foil

coordinates
at E
p
=420

MeV. The data, in units of
k
Bq/g
, are from Run 3



Z

[mm]






R

[mm]




25


55


85


125


155


76


489

3



551

4


641

4


514

3


472

3


126


256

2


288

2


326

2


247

2


229

1


176


91.2

0.6


102.0

0.6


117.0

0.7


88.3

0.5




226


31.0

0.2


34.3

0.2


39.0

0.2


30.2

0.2







Table

3b: Measured

56
Mn

activities

without

Cd

cover

as

function

of

radial

(
R
)

and

axial

(
Z
)

foil coordinates


at E
p
=420

MeV. The data, in units of
kBq/g
, are from Run 3


Z

[mm]






R

[mm]




25


55


85


125


155


76

4450

20

4960

25

5190

25

4200

20

3880

20


126

2180

10

2440

10

2740

15

2080

15

2060

15




Table

4a:

Measured

198
Au

activities

without

Cd

cover

as

function

of

radial

(
R
)

and

axial

(
Z
)

foil

coordinates
at E
p
=590

Me
V. The data, in units of
kBq/g
, are from Run 4



Z

[mm]






R

[mm]




25


55


85


125


155


175


205


235


265


295


76

1220

10

1410

10

1460

10

1460

10

1320

10

1290

10

1090

10

880

10

675

5

495

5


126


645

5


730

5


755

5


735

5


655

5












176


241

1


268

2


282

3


265

3


246

2












226


83

1


95

1


96

1


92

1


87

1















Table

4b:

Measured

56
Mn

activities

without

Cd

cover

as

function

of

radial

(
R
)

and

axial

(
Z
)

foil

coordinates
at E
p
=590

MeV. The dat
a, in units of
kBq/g
, are from Run 4

Z

[mm]





R

[mm]




25


55


85


125


155


175


205


235


265


295


76

9870

40

11400

50

11950

60

11828

60

10750

50

10620

60

8940

50

7230

35

5630

30

4143

20


126

5380

20


6110

20


6
330

30


6130

30



5560

30















The

specific activity data at
E
p
=300

MeV

(Tables 2a, 2b), 420

MeV (Tables

3a,

3b) &
590

MeV

(Tables 4a, 4b)

are
displayed in Figs. 5, 6 & 7, respectively. Via the energy
-
dependence of the capture cross
-
section,

each foil
-
type
exhibits

a

characteristic

sensitivity

to

the

slow
-
neutron spectrum [76] within

the

water

moderator.

Broadly speaking,
the Mn foil activities are almost entirely due to thermal neutrons, whereas the Au foil activities receive a 15
-
30%
contri
bution from epithermal neutrons. However, the Au slow
-
neutron capture cross
-
sections are known much more
precisely (0.15%
-

[59]) than the corresponding ones for Mn (1.5%
-

[92]). Thus, only the
198
Au activity data have
been used for deriving experim
ental values for

n/p

(see sections 3.4, 3.6). The
56
Mn data presented here will be
discussed in the context of neutron code validation (objective #3 in the Introduction) in a separate publication.


9


Fig. 5

Activity

distributions

of

198
Au

with

(open

poin
ts)

&

without

(solid

points)

Cd

cover

at

E
p

=

300

MeV.
For

display

reasons,

activities

of

foils

with Cd cover

(Table 2b) have

been

multiplied

by

a

factor

of

5.
The

proton

range

at

this

energy

in

a

Pb/Bi

target

(~95

mm)

is

indicated

by

the

vertical

dot
-
dash
ed

line.







Fig. 6 Activity distributions of
198
Au (solid points) &
56
Mn (open points) at E
p

= 420 MeV. For display
purposes, activities quoted in Tables 3a, 3b have been multiplied by a factor of 5. The proton range
in

the Pb/Bi target

at

this

bom
barding

energy (~160

mm) is

indicated

by

the vertical dot
-
dashed line.





100
1000
10000
100000
0
25
50
75
100
125
150
175
axial coordinate
Z

in mm
specific activity

in

kBq

/

g
R
(
Au
) =
76
mm
R
(
Au
) =
126
mm
R
(
Au
) =
176
mm
R
(
Au
) =
226
mm
R
(
Mn
) =
76
mm
R
(
Mn
) =
126
mm

10
100
1000
0
25
50
75
100
125
150
175
axial coordinate Z


in mm
specific activity

in kBq

/

g
R
=
76
mm
R
=
126
mm
R
=
176
mm
R
=
226
mm
R
=
76
mm
(+
Cd
)
R
=
126
mm
(+
Cd
)
R
=
176
mm
(+
Cd
)
Series
3

10


Fig. 7 Activity distributions of
198
Au (solid points) &
56
Mn (open points) at E
p

= 590 MeV. For display
purposes, activities quoted in Tables 4a, 4b have been multiplied by a f
actor of 5.

The proton range
in a Pb/Bi target at this bombarding energy (~275 mm) is indicated by the vertical dot
-
dashed line.



As evident from Figs. 5

-

7, the overall extension of the neutron radiation source increases and the peak activities are
dis
placed to higher
Z
-
values when the incident proton energy
E
p

is raised. Furthermore, the
Z
-
dependence of the
activity distributions is seen to be most pronounced at the closest foil locations (
R

= 76

mm).


This

reflects

the fact
that

the

features

of
the

initial fast
-
neutron distribution

are

gradually effaced

as the water thickness traversed

increases.


The
R
-
dependence of the activity distribution primarily reflects the thermalization properties of the water.


Indeed, the
300 MeV data in Fig. 5 exhi
bit a faster falloff with increasing
R

for Cd
-
covered foils than for uncovered foils, reflecting
a reduction in the activity contribution from epithermal neutrons.


Quantitatively, the Au Cd
-
ratio [76]

for the 300

MeV run can

be

read

off Fig. 5 for

all co
rresponding pairs of data

points.
Table

5 displays the slow
-
neutron properties as function of the water depth (
=
R



50
, in mm) traversed by the
neutrons at 300

MeV.

It shows

that the Cd
-
ratio goes up as the water depth increases and that
Φ
thermal
/

Φ
epithermal
,
the ratio of thermal to epithermal flux, is accordingly enhanced.



Table 5: Slow
-
neutron

properties

as

function of water depth


R

[mm]



E
p

[MeV]


<
R
A
meas
/
calc

>


n/p
meas


n/p
calc



420



??




6.0


0.5


??





590



??




9.6


0.7


??



76


126

176



Water depth


26


76

126

Au Cd
-
ratio


~5


~5


~7


~9

Φ
thermal

/

Φ
epithermal


~60


~90


~120



3.4
Procedure for deriving
n/p
meas

The

total

number

of

neutrons emitted

per

incident

proton

n/p

is

determined

from

the

spatially
-
sampled distribution

of

measured
198
Au

specific

activities.

The latter

essentially

represents

the

slow
-
neutron

fluence

distribution

in

the

water

surrounding

the

target. In the conventional variants

o
f the water
-
bath method [49], the spatial fluence distribution is
experimentally

integrated over 4


in

order

to

yield

the

total

n/p

value.


100
1000
10000
100000
0
50
100
150
200
250
300
axial coordinate
Z

in mm
specific activity

in kBq

/

g
R
(
Au
) =
76
mm
R
(
Au
) =
126
mm
R
(
Au
) =
176
mm
R
(
Au
) =
226
mm
R
(
Mn
) =
76
mm
R
(
Mn
) =
126
mm

11

However,

in

the

present

work

a

somewhat

different

procedure, representing a novel variant of the water bath method,

was

adopted:

n/p
meas

was

derived

with

the

aid

of

MCNPX [60],

a multi
-
particle Monte
-
Carlo code th
at quantitatively
simulates the

totality of nuclear interactions in the full experimental setup, including plexiglass housing, target, water
moderator and activation foils. It essentially consists in scaling the MCNPX
-
computed value
n/p
calc

by means of

the
average ratio of measured to MCNPX
-
computed
198
Au activities. This circumvents the problematic 4

-
integration




a

non
-
trivial

issue for

extended

radiation

sources




since it

is

the

simulation

code

that relates the

slow
-
neutron fluence
distribution, sampled over a relatively small set of spatial locations, to the integral quantity

n/p

.


In pract
ice, the procedure for assigning
n/p
meas

values to the
198
Au activity distributions (which represent the measured
neutron fluences) involved the following sequence of operations:


a.

The
198
Au specific activities (without Cd
-
cover) of sect. 3.3 were divided b
y the values of N
p
tot

of sect. 3.1,
thereby generating a spatially
-
sampled distribution of

measured

specific activities per incident proton


b.

MCNPX was applied to generate a corresponding grid of

calculated

198
Au specific activities per incident
proton, a
s well as to calculate the overall number of neutrons per incident proton
n/p
calc


c.

The measured
198
Au specific activity per proton (see (a), above) at each foil location (
R

i
,

Z

i
)

was divided
by the MCNPX
-
determined value at that location (see (b), above
), yielding a ratio
R
A
meas
/
calc
(
R

i
,

Z

i
)


d.

A weighted
-
average

of

these

ratios
<
R
A
meas
/
calc

>

was taken

over the points (
R

i
,

Z

i
) on

the spatially
-
sampled distribution


e.

The

experimental value


n/p
meas


was

determined from the following equation:


n/p
me
as


=

n/p
calc



<
R
A
meas
/
calc

>





(3.4.1)


It is noteworthy that this procedure is

highly insensitive

to the value the code assigns to

n/p
calc

(and to its error)
, since
the product of the two terms in eq. (3.
4
.1) effectively cancels out the

dependence on this quantity,

provided that

MCNPX
reproduces well the

shape

of the slow
-
neutron fluence distribution and predicts its approximate

magnitude
.

However, there remains the question of demonstrating that the

procedure

is

free

of

systematic

erro
rs.

This will clearly
be the case

only

if

the

code

reliably

predicts

the

principal nuclear

interactions that cannot be directly inferred from the
activation
-
foil data.

The latter pertain primarily to:


1.

the spectral and angular distributions of fast neut
rons emitted in the multiple spallation processes that occur
in the thick target


2.

the moderating processes undergone by such neutrons in the water surrounding the target


Since

MCNPX

and its forerunner codes have

been well

benchmarked

with

respect

to

(2),
the

soundness

of the

procedure is predominantly contingent on the code’s performance with respect to (1).

This topic is addressed in the
following section, along with the salient features of the MCNPX code relevant to the present context.



3.5
MCNPX
: code description and verification

A few years ago, Los Alamos National Laboratory released MCNPX version 2.1.5 [60], a Monte
-
Carlo simulation code
that fully integrates the high
-
energy particle transport capabilities of LAHET 2.8 [57] with the low
-
energ
y neutron
transport code MCNP4B [59]. The most important feature of MCNPX invoked here is continuous tracking of neutrons
from the initial reaction that produces them until they are absorbed or escape the experimental setup.


MCNPX

is

also

capable

of

uti
lizing

evaluated

cross
-
section

data

libraries, such

as LA150n
[61]

in

the

energy

range E
p

=

20

-

150

MeV,
where the INC models are of questionable validity.



The work described here was based on MCNPX
version

2.1.5, along with
LA150n

for neutrons, nuclear

interactions of
protons, muons and pions being treated within LAHET. The code
-
option parameters were chosen such that all
particles switch from the Bertini INC model [51] to the ISABEL model [52] at 500 MeV.



12

The entire experimental water bath set
-
up (i
ncluding the detailed beam/target/water
-
bath/activation
-
foil configurations)
was rigorously modelled using the capabilities of MCNP4B. Data from ENDF/B
-
VI.1
[59]
were used for gold
-
foil
neutron
-
activation, not explicitly modelled as the cross
-
sections ar
e not yet available in the LA150n library.


To verify the code performance (see sect 3.4), several of its predictions are presented and discussed below, in
comparison to measured values.


1.

A comparison has been made to recent double
-
differential (wi
th respect to energy and angle) neutron
-
yield
data for 500

MeV protons on 20

cm thick Pb targets [35]. The relevance of this comparison is twofold:

a)


it tests MCNPX’s predictions for the properties of fast neutrons emitted in the primary spallation re
action

b)


it tests MCNPX’s handling of the complex multiple interactions that subsequently occur in the thick target


To

this

end, simulated MCNPX neutron spectra and yields

have

been

compared to measured values at
51
o
, 60
o
,
120
o
, graphically reconstructed
from Fig. 8 of [35]. The results of this comparison are displayed in Fig. 8 below.




Fig. 8

Fast
-
neutron yield distributions for 500

MeV protons on a 20

cm thick Pb
-
target at 3
measuring angles, comparing the results of a computer simulation using
MCNPX
-
2.1.5 (this
work, continuous lines) to experimental data (ref. [35], discrete points). For display
purposes, the yields at 15
o

& 120
o

have been multiplied by factors of 10
2

& 10
-
2
, respectively.

As evident from Fig. 8, MCNPX 2.1.5 reproduces the ov
erall yield magnitudes and anisotropies quite well, though
local discrepancies, particularly in the 20



80

MeV region, may be as large as a factor of 2 in extreme cases.
However, the comparison also shows that such local discrepancies are, to a certain
extent, compensated over
broad energy intervals. Table 6 displays a quantitative comparison of simulated and measured yields, in that
the values of Fig. 8 (nota bene: per MeV neutron
-
energy) have been integrated over several E
-
bins, as follows:

Bin
I
:



E
n

<

1.4

MeV,



containing most evaporation neutrons [54] below the exp. threshold of [35] (MCNPX only)

Bin
II
: 1.4

<

E
n

<

5

MeV
,

containing most evaporation neutrons [54] above the experimental threshold of [35]

Bin
III
: 5

<

E
n

<

20

MeV
, co
ntaining most of the
readily
-
thermalized, low
-
E
n

intra
-
nuclear
-
cascade neutrons [50
-
53]

Bin
IV
: 20

MeV < E
n

,


containing the
less
-
readily
-
thermalized, h
igh
-
E
n

intra
-
nuclear
-
cascade neutrons

Bin
V
: 1.4

MeV
< E
n
,

containing the sum of
bins

II
,
I
II

&
IV

Bin
VI
:
Total

,

containing the sum of
bins

I

&
V

(MCNPX only)

1
.
0
E
-
07
1
.
0
E
-
06
1
.
0
E
-
05
1
.
0
E
-
04
1
.
0
E
-
03
1
.
0
E
-
02
1
.
0
E
-
01
1
.
0
E
+
00
1
.
0
E
+
01
1
.
0
E
+
00
1
.
0
E
+
01
1
.
0
E
+
02
1
.
0
E
+
03
E
n

in MeV
Neutron Yield
in

n
x
MeV

-
1
X

sr

-
1
X

p

-
1
15
o
(
x
100
)


60
o
(
x
1
)

120
o
(
x
0
.
01
)

13

Table

6:

Comparison

of

differential

neutron

yields

at

500

MeV


MCNPX

2.1.5

vs.

thick

target

data



Source


Theta

Di f f er ent i al neut r on yi el d i n ener gy bi n


[ n/sr/p]


I
:


E
n

<

1.4

MeV


II
:

1.4

<

E
n

<

5MeV


III
:

5

<

E
n

<

20

MeV


IV
:


20

MeV

<

E
n


V
:
1.4

MeV

<

E
n

VI
:

Total









MCNPX


15
o


0.22
±

0.02


0.166
±

0.005


0.045
±

0.001


0.109
±

0.004


0.32
±

0.01

0.54

±

0.03

Ref. [35]




0.147
±

0.005


0.047
±

0.001


0.119
±

0.004


0.31
±

0.01











MCNPX


60
o


0.27
±

0.02


0.213
±

0.006


0.054
±

0.002


0.064
±

0.002


0.33
±

0.01

0.60

±

0.03

Ref. [35]




0.196
±

0.006


0.
0
6
2

±

0.002


0.073
±

0.002


0.33
±

0.01











MCNPX


120
o


0.31
±

0.02


0.239
±

0.007


0.050
±

0.002


0.018
±

0.001


0.31
±

0.01

0.62

±

0.03

Ref. [35]




0.212
±

0.006


0.060
±

0.002


0.021
±

0.001


0.29
±

0.01



where the 3% errors quoted reflect both the estimated experimental pre
cision of the cross
-
section database
underlying MCNPX, as well as the reliability of the graphic reconstruction performed on the data of [35].

As evident from Table 6,
MCNPX 2.1.5 indeed reproduces the anisotropies and trends with neutron energy rather
wel
l. It slightly overestimates

the values in
bin
II,
but underestimates those in
bins

III

&

IV

by approximately
the same margin. Consequently, the total yields above the experimental threshold of ref [35] are in excellent
agreement with the data. In
bin

I

there is no data to compare, but the MCNPX values quoted allow computation
of the total neutron/proton angular yield (
bin
VI
). The latter values serve as a further test on the veracity of
MCNPX predictions (see point (2) below).

To summarize poin
t (1), the values and errors quoted in Table 6 clearly demonstrate that the yields and
anisotropies predicted by MCNPX 2.1.5 are adequately consistent with the data of [35] to validate the procedure
for determining
n/p
meas


described in the previous secti
on.

2. The total, angle
-
integrated neutron yield
n/p

predicted by MCNPX serves as a further check on its reliability.

From the total yields

predicted by the code at each angle (
bin
VI

in Table 6
)
, a total value
n/p ~7.5

may be
inferred for a thick P
b
-
target bombarded by 500 MeV protons. This value is in excellent agreement with the
experimental systematics presented in Figs. 9 & 10 below.

3. With respect to the water
-
bath data of the present work, MCNPX predicts that at 420 & 590

MeV respectivel
y,
99.8% & 99.1% of all protons (primary and secondary) stop in the target, the rest escaping into

the

water.


These

values

agree

with

systematically
-
measured

[7,37
-
40]

and

LAHET/MCNP
-
calculated

[57,66,93]

n/p

yields

as

function

of

target

diameter,

tha
t

clearly

scale with

the

number

of

primary
,

and

higher
-
order

protons

stopping

in

the

target. These

saturate

at target diameters > ~100

mm at

these

incident

energies.


As

E
p

goes

up,

the

yield
-
saturating

diameter

also

increases

[37
-
40].

Based on point
s (1), (2) & (3), the overall conclusion of this section is that the predictions of MCNPX 2.1.5 have been
verified to a sufficiently stringent degree in the relevant proton energy range, thereby ensuring that no code
-
related
systematic error is introduced
into the values assigned to
n/p
meas

in the following section.


3.6
n/p
meas

assignments

The procedure outlined in sect. 3.4 was applied to the 420 & 590 MeV
198
Au activity data, for which the total number of
incident

protons

per

irradiation

were

accu
rately

determined

(sect. 3.1).

Tables 7 & 8 display the values of
R
A
meas
/
calc

for the close
-
in (low
-
R
) radial foil
-
coordinates at 420 & 590 MeV, respectively.

At the

higher
-
R

foil
-
coordinates, the
MCNPX
-
calculated
198
Au activities were not determi
ned with sufficient precision to be of use in deriving
n/p

.





Table 7:

Spatially
-
sampled distribution of
R
A
meas
/
calc

198
Au
-
activity ratios


at 420

MeV



Z

[mm]






R

[mm]




25


55


85


125


155


76

1.11
±
0.06

1.03
±
0.05

1.20
±0.06

1.08
±0.06

1.12
±0.06


126

1.17
±0.09

1.14
±0.08

1.39
±0.11

1.14
±0.09

1.34
±0.13


14

Table 8:

Spatially
-
sampled distribution of


R
A
meas
/
calc

198
Au
-
activity rat
ios


at 590

MeV


Z

[mm]






R

[mm]




25


55


85


125


155


175


205


235


265


295


76

1.10
±
0.05

1.01
±0.05

1.05
±0.05

1.00
±0.05

1.02
±0.05

1.03
±0.05

1.21
±0.09

1.05
±0.08

1.15
±0.09

1.28
±0.11


126

1.15
±0.09

1.11
±0.08

0.94
±0.06

1
.14
±0.09

1.01
±0.08












The
1




errors quoted on the
R
A
meas
/
calc

values of Tables 7 & 8 are dominated by the event statistics of the MCNPX
simulation, which was performed with

4∙10

6

& 5∙10

6

protons incident on the target at 420 & 590 MeV,
respectively.

Following the procedure outlined above,

the weighted means of these ratios, their variances and


values⁡e:







<
R
A
meas/calc

>

=

1.13

± 0.03


(


=1⸷5)



at 420 MeV







<
R
A
meas/calc

>

=

1.
0
5

± 0.02


(


=1⸴2)


at 590 MeV

Evidently, MCNPX does reproduce the
shape

of the fluence distribution rather well, since the variances quoted above
exceed the mean (statistical, internal) errors by



, or no more than

32%

&

19% at 420

&

590 MeV, respectively.

Moreover, the code also reproduces the approximate magnitude of the overall neutron yields, as manifest by the
relatively small departures of

<
R
A
meas/calc

>

from unity.

The slightly larger value of

<
R
A
meas/calc

>
at 420

MeV
compared to 590

MeV would

appear to indicate that MCNPX version 2.1.5 reproduces the measured spallation
neutron yields somewhat less well at the lower incident energy.

From these results and findings, it is concluded that the conditions for deriving the values of
n/p
meas

from

eq. (3.4.1)
via the procedure described above and in sections 3.4 & 3.5 are indeed fulfilled at both incident proton energies.


With these values for
<
R
A
meas
/
calc

>
and with the MCNPX
-
calculated quantities:


n/p
calc


=

5.3







at 420 MeV

n/p
c
alc


=

9.2






at 590 MeV

where the uncertainties on

n/p
calc

(a few percent, primarily

representing

the

errors

on

the

cross
-
section

data used in
MCNPX)

are

not

quoted, since

the

dependence

on this quantity is effectively cancelled

out (see comm
ent to eq. 3.4.1).

Thus, the procedure outlined in sect. 3.4 yields:

n/p
meas

=

6.0



0.3


(1



limits)




at 420 MeV

n/p
meas

=

9.6



0.4


“ “





at 590 MeV

where

the individual sources of uncertainty that contribute to the e
rror on
n/p
meas

are as follows:



measured cross
-
section for
27
Al(p,3n3p)
22
Na (adopted average)









4

% [43, 80
-
87]



measured specific activities of
22
Na







< 1

%



recoil loss corrections to
22
Na data







< 0.1

%



measured sp
ecific activities of
198
Au







0.7

-

1.0

%



precision of measured
197
Au slow
-
neutron capture cross
-
sections





0.15% [59]



mean error on
n/p
calc

due to MCNPX event statistics







< 0.02%



total MCNPX variances on c
alculated
198
Au activities


3

% (420MeV) &

2

%
(590MeV)

Propagating these uncertainties in quadrature yields overall relative errors of
5.1

%

and
4.3

%

for the
n/p
meas

values at 420

MeV & 590

MeV , respectively.

They

correspond to the 1



limit errors quoted above.


With respect to the 300 MeV data, it was not possible to assign a value of
n/p
meas
, since the total number of protons in
the irradiations, N
p
tot

, remain as yet undetermined ( see sect. 3.I).



15

4. Discussion

4.1
The
n/p

va
lues and their E
p
-
dependence

Despite

the

considerable

volume

of experimental

and theoretical work

on

proton
-
induced

spallation with

high
-
Z targets
and the importance of the latter for existing and planned high
-
current neutron facilities
,
no comprehensive,
up
-
to
-
date
compilation of neutron yield data on thick Pb and Pb/Bi targets is to be found in the recent literature
. Hence, an
extensive survey
of total
-
neutron
-
yield measurements for thick Pb
-
targets as function of incident proton energy

was
made in
the
present work.

Figs. 9 & 10 display the subset of total
n/p

data in the 100

MeV
-

1

GeV range and the
full set

of

results

in

the 10

MeV
-

5

GeV range,

respectively.


They

include

values

obtained

in

older

measurements

[21
-
28], recent data from neutron
-
mul
tiplicity studies [36
-
40], as well as the values determined here.


Such data
-
pooling is possible because

n/p


is related to the mean neutron
-
multiplicity
M
n

via:










n/p(E
p
) = M
n
(E
p
) ∙
P

(E
p
)













(4.1
.1)



where

P

(E
p
)
, the nuclear interaction probability for a proton incident on the target at energy
E
p
,

is given by:








P

(E
p
)


=

1


exp (

-




reaction





)












(4.1.2)




reaction

being

the

total

reaction

cross
-
section

and


the

target

areal

density

at

the

proton

electronic
-
stopping

range

[79].


Rigorously, eq. 4.1.1 is only valid for thin targets, or single interactions in thick targets at relatively low
-
E
p

, for which
P

<< 1

, such that the target is “optically thin” and e
q. 4.1.2 can be linearized.


Nevertheless, to a good approximation,
it is also valid for “optically thick” targets, with the caveat that

n/p
and

M
n


depend to some extent on target
-
diameter
and thickness (even beyond the proton range) due to multiple nucl
ear interaction contributions. However, these
target dimensions are found to exhibit yield
-
saturating values [37
-
40], beyond which they no longer vary appreciably.


Thus, for self
-
consistency reasons,

each

data point

in Figs. 9 & 10 has been extrapola
ted to a target thickness
corresponding to the electronic
-
stopping range and to the yield
-
saturating target diameter [37
-
40] at the incident
proton energy in question. In no case did the extrapolation procedure involve corrections of more than a few perc
ent.
The only exceptions to this convention are the data from [24], in which a very thick target was employed
(approximately twice the proton range at the highest energy). These data are presented as taken.


Methodologically, presenting the poole
d
n/p
and

M
n

results has the distinct advantage of allowing comparison of
data obtained with substantially different experimental techniques.




F
ig. 9 Compilation of thick
-
target
n/p

values for
p

+

Pb

&

Pb/Bi

measured to date at interme
diate
-
E
p

.

0
3
6
9
12
15
18
0
100
200
300
400
500
600
700
800
900
1000
E
p

[
MeV
]
neutron yield per proton
Fraser et al
-
1965
[
23
]
Vasilkov et al
-
1968
[
24
]
West et al
-
1971
[
25
]
Lone et al
-
1983
[
26
]
Ryabov et al
-
1983
[
27
]
Lott et al
-
1997
[
39
]
Letourneau et al
-
2000
[
40
]
Present Work
(
Pb
-
Bi
)

16

As seen in Fig. 9, the data of the present work (red circles) fall well within the range of values from recent multiplicity
studies [39
-
40] and older

activation

analysis

data

[23
-
27].

The

slightly

higher

values

obtained

in

[24]

might be due to

the very long target used in those experiments, since the excess thickness beyond the proton range can enhance the
neutron yield to some extent, via (n,xn) processes undergone by energetic, forward
-
going neutrons on Pb, Bi nuclei.


F
ig. 10 Compilation

of

thick
-
target


n/p


values

for
p

+

Pb

&

Pb/Bi

measured

to

date

at

all

incident

energies.


As illustrated in Fig. 10, the salient features of the full set of measured thick
-
target neutron yields are as follows:

1.


the remarkable overall consistency

of

the

data

and the

regularity

of

their

energy
-
dependence


2.

the
E
p
-
dependence of the yield is strongest at low energies and progressively weakens as
E
p

increases

3.

Specifically, in the 20
-

100

MeV range, the yield is found to vary approximately as
E
p
3

4.

In the 100
-

1000

MeV range, the yield is found to vary approximately as
E
p
1.5

5.

In the 1
-

4

GeV range, the yield is found to vary approximately as
E
p
0.7

In a broader context, the magnitude and

E
p
-
dependence of spallation processes, both with respect to individual
rad
ionuclide production and integral
-
neutron yields, have been the subject of numerous systematic analyses over the
years (see, e.g., [50
-
53, 58, 75, 94
-
97] and refs. therein). The latter have given rise to a number of semi
-
empirical
formulae of varying co
mplexity, applicability range and inherent accuracy in predicting the physical quantities.


However, in the low
-
energy nuclear reaction range (20
-

100

MeV), the
E
p
-
dependence can be
phenomenologically
explained on quite general terms, without recourse to
any specific nuclear reaction model. At these energies,
multiple interactions can be neglected and eq. 4.1.2 for the nuclear interaction probability
P

of a beam proton in the
target

can be linearized to:







P




reaction












(4.1.3)


and thus, one obtains the simple relation:


n/p


M
n




reaction










(4.1.4)



At these proton energies, the
E
p
-
dependence of these quantities is known to be as follows:

a)

The mean neutron multip
licity
M
n

increases approximately linearly with
E
p


[36
-
40]

b)

The total reaction cross
-
section


reaction


typically increases proportionally to
E
p
0.3

-

0⸶

[98
-
102]

c)

The target areal density at the proton range


inceases⁡pp牯ima瑥ly⁰牯po牴onal

E
p
1.7


[79]

0
.
001
0
.
01
0
.
1
1
10
100
10
100
1000
10000
E
p

[
MeV
]
neutron yield per proton
Tai et al
-
1958
[
21
]
Fraser et al
-
1965
[
23
]
Vasilkov et al
-
1968
[
24
]
West et al
-
1971
[
25
]
Lone et al
-
1983
[
26
]
Ryabov et al
-
1983
[
27
]
Hilscher et al
-
1998
[
38
]
Lott et al
-
1997
[
39
]
Letourneau et al
-
2000
[
40
]
Present Work
(
Pb
-
Bi
)

17

Substituting these energy
-
dependences into eq.

4.1.4, one indeed reproduces the observed overall
E
p
-
dependence:



n/p

=
const


E
p
3

-

3.3

As for the
E
p
-
dependence at higher incident proton energies (100

MeV
-

5 GeV),

d)

The

mean

neutron

multiplicity

M
n

for

thick

targets

continues

to

increase

approximately

linearly

with

E
p

[36
-
40]

e)

The

total

reaction

cross
-
section


reaction


is

essentially

constant at

~1.8

b, at least up to 1.5

GeV

[47,98
-
102]

f)

The target areal density at the proton rang
e


continues⁴o⁩nc牥aseⰠapp牯ima瑥ly⁷i瑨
E
p
1.1

-

1.5

[79]

As a consequence of (e) & (f), the overall interaction probability

P

(E

p
)


in eq. 4.1.2 will tend to saturate (all protons
undergo nuclear reactions) at proton energies
E
p

>

~600

MeV.

Thus
, the
E
p
-
dependence of
n/p

(eq. 4.1.1) will
progressively weaken with increasing proton energy, asymptotically coinciding with that of the mean thick
-
target
multiplicity
M
n
, as indeed, experiment shows (Fig. 10 and features 4, 5 above).


5.

Summary

Spallation
-
neutron

yields

for

protons

at

E
p

=

300,

420

&

590

MeV

incident

on

thick

Pb/Bi

targets

have

been

determined
via

activation

analysis

of Au

& Mn foils

at

the

PSI

cyclotron.

The data were obtained with the water
-
bath method, in a
novel variant t
hat incorporates a detailed MCNPX simulation in the analysis procedure.

The measurements were
performed over an extensive grid of spatial locations in the water surrounding the target.


At E
p

=

300

MeV,
198
Au

activities

were

measured

for

both

bare

an
d

Cd
-
covered foils, yielding activity distributions and
Cd ratios as function of water depth traversed by the neutrons. At E
p

=

420

&

590

MeV, both
198
Au &
56
Mn

activities
were

measured.


Up

to

an

overall

scaling

factor,

these

activities

represent

two

different

weighted
-
averages

of

the

slow
-

neutron (thermal and epithermal) fluence distribution. The

precision

achieved

in

these

measurements was 0.7
-
1.5%
per point.


With the aid of a computer
-
simulation using MCNPX version 2.1.5, the slow
-
neutron fl
uence distribution determined
via Au foil activation was analysed to derive total

spallation
-
neutron

yields per proton.

The procedure yielded
n/p

values at

420

&

590

MeV,

respectively.

At 300

MeV, the number of incident protons in the irradiation rema
ins
undetermined at present, so that no value for
n/p

can be quoted at this energy.


An

extensive

literature

survey of

n/p

and neutron
-
multiplicity data for thick Pb targets shows

that

the yield

values
measured in the present work fall

well

within

the

range

of the

experimental systematics.


The latter exhibits
remarkable regularity over proton bombarding energies from ~20

MeV to ~5

GeV, its energy dependence steadily
decreasing from E
p
3

at the lowest energies to E
p
0.7
at the highest.


The

results

of

the

present

work

contribute

to

the

database

of nuclear quantities

pertinent to the

design

and

optimization
of new, high
-
intensity spallation
-
neutron sources at low
-
to
-
intermediate beam energies. They should permit accurate
benchmarking

and

detailed

i
nter
-
comparison

of

simulation
-
code

predictions

at

incident

proton

energies

E
p

<

~400

MeV,
where the theoretical understanding of the spallation reaction mechanism

is

not yet

on

a

firm

basis.



Acknowledgments

This work was performed at the Proton Accelerat
or of the Paul
-
Scherrer
-
Institut, Switzerland.


The authors would like to thank Drs. David Vartsky and Gideon Engler for many productive discussions and helpful
comments. We are very much obliged to the PSI management and especially Professor Ralph Eichl
er for his
unequivocal support and encouragement throughout this project. The PSI accelerator operating staff, SU,
Hallendienst and Electronics Pool personnel gave us outstanding assistance throughout all measurements.



18

References

1.

J.M. Carpenter, Nucl. I
nstr. & Meth.,
145

(1977) 91

2.

D. Goutte, S. Leray & J.
-
L. Boutard, “La spallation et ses applications”, Clefs,
37

(1997/98)

3.

“The ESS Project”, Vols. I
-

III (ed. D. Richter, ESS Central Project Team, c/o FZ
-
Jülich, May 2002) &
www.fz
-
juelich.de/ESS/

4.

J.
Alonzo, “The Spallation Source (SNS) Project Accelerator System at Oak
-
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