An alpha-recoil spectrometer

NUCLEAR

INSTRUMENTS

AND METHODS

165 ( 1 9 7 9 ) 5 0 9 - 5 1 6 ,

(~) N O R T H - H O L L A N D

PUBLISHING

CO

AN ALPHA-RECOIL SPECTROMETER PATRICK J McDANIEL* and H E HUNGERFORD

Department of Nuclear Engmeermg, Purdue Umverstty, West Lafayette, IN, U S .4 Recewed 7 February 1979 A gas-propomonal counter ~s described which measures fast-neutron spectra using the recods of hehum nucle~ scattered by neutrons The resulting s~gnal ~s unfolded using a matnx-mvers~on techmque Theory and experimental results are included

1. Introduction Gas propomonal proton-recod spectrometers are relatively widely used for the measurement of fast reactor neutron spectra 1,2) They are small m saze, relatavely sturdy, and possess a reasonable efficaency for this type of measurement They do not appear to perturb the measured envaronment sagnlficantly and can provade very good resolutaon from around 1 0 keV to 1 0-2 0 MeV Thear major hmltatlon appears to be the maximum energy measurable wathout severe dastomons of the recoil spectrum due to recod track truncataon by the boundaries of the detector sensatwe volume Typacally energaes of the order of 1 0 to 2 0 MeV have been the haghest obtainable without a major pomon of the recod track terminating prematurely on the boundaries of the sensatave volume An obvaous extensaon of the proton-recod spectrometer is the alpha-recod spectrometer It can obtain sagnlficantly higher energaes as a gas propomonal counter because of two major differences in the recod generataon process The maximum energy that can be transferred to an alpha recoil by a neutron is 64% of the neutron's energy, as opposed to 100% for a proton recod The range of alpha recoils an typical gas counters is consaderably shorter than the range of proton recods Therefore at as possable to measure neutron spectra m the hagh fission (and possably fusaon) energy range wath an alpha-recoil spectrometer Spectrometers are available that cover thas energy range but they are generally not compaUble wath a gas proportional proton-recod system l'he hqmd scintillators are generally considerably larger and therefore are not statable for "wathln-the-

reactor" measurements 3) The associated photomultiplier tubes are also quite sensitive to the mtense gamma ray backgrounds involved The semaconductor spectrometers tend to have qmte a bat lower efficaency than gas counters and thear dlrectaonal responses are more difficult to calculate 4) Neither type of spectrometer has been used wath an unfoldang scheme that is compatible wath extensaons to lower energaes on a loganthmac energy scale Therefore an alpha-recotl spectrometer appears to be an adeal devace for extending neutron spectrum measurements to the 10 to 20 MeV range It IS quite compatable wath lower energy proton recoil measurements and can be used wath nearly all of the same electromc system components It does have two major hmltataons however- Farst, resolution effects that do not vary with the energy of the detected pamcle, such as electromc noase, or pile up effect, have a much greater perturbataon on the measured alpha-recod spectrum than they would be to a slmdar proton-recod spectrum Second, the scattering of neutrons by hehum nuclea as not asotropac m the center of mass system Thas means that simple dffferentlataon procedures, commonly employed with proton-recoil spectrometers, become quite comphcated af attempted wath an alpha-recoil spectrometer In the present investigation a matrix reversion approach has been taken, and the unfolding as no more comphcated for the alpha-recod spectrometer than for the proton-recod spectrometer In fact the coupling of the measurements from the two spectrometers as accomphshed qmte easily during the matrtx generataon process

2. Description of detector and electronic system Two detectors of a standard desagn* were used * Present address USA

Sandm Laboratories, Albuquerque, NM,

* Detectors were purchased from LND, Inc, 3230 Lawson Blvd, Oceanstde, NY 11572

510

P

J

McDANIEL AND H

E

HUNGERFORD

TABLE 1 Detector gas composlt~ons, pressure in atmospheres Detector a

H2

CH4

3 He

4 He

N2

CO 2

Kr

Total

H10 HE20 HE6

10 0 -

0 36 -

0 002

20 0 60

20 20 0

0 72 0 42

20 80

12 4 24 7 14 4

a T h e n u m b e r s after the symbol indicate major gas pressure

for the alpha-recoil measurerr,ents A cross sectional wew is presented in fig 1 The sens~twe volume ~s 2.54 cm long by 1 092 cm m dmmeter The central anode ~s 0 00254 cm m dmmeter The filhng gas pressures for both detectors and a compatible proton-recod detector are presented m table 1 The h~gh pressure alpha recod detector HE20 (20atm 4He) was purchased first and a large amount of mtrogen was included as a cahbratson gas Thermal neutrons reacting w~th ]4N produce a mono-energet~c event corresponding to 626 keV of energy deposited in the detector Previous work on the PUR-I reactor s) had indicated that the pressure ratios selected for the HE20 detector would produce a cahbratlon peak visible above the high energy recoil background when th~s detector was lrradmted near the PUR-I reflector However during the mvest~gatton it became obvious that thin large quantity of mtrogen would prod/ace severe dmtort~ons m the unfolded spectrum Therefore, 3He was chosen as the cahbrat~on gas for the second detector, HE6. The thermal reaction w~th 3He produces a mono-energet~c event correspondmg to an energy of 764 keV Early problems with obtaining adequate resolution from the HE20 detector seemed to mdtcate that the total gas pressure had to be lowered to obtain a better resolution Thus the total pressure for the HE6 detector was set at 14 4 atm and the relative hehum-krypton m~xture was selected to develop an adequate recoil response up to 10 0 MeV Krypton was added to both detectors to increase the stopping power of the m~xtures Krypton recoils are neglected m the unfolding process as

they occur at a constderably lower energy than the helium recoils Carbon dioxide was added to both detectors as a quenching agent It also serves to speed the electron collection process and therefore improve resolution The electronic system used is presented in fig 2 The charge-sensitive preamphfier used was built from a design by Larson 6) It contributed negligible electromc no~se to all spectrum measurements The dominant source of resolution broadening appeared to be pile up effects m the h~gh gamma ray backgrounds measured Th~s could have been reduced by using a shorter shaping t~me constant to hmlt the system amphfier's bandwidth However, analog s~mulat~on studies of the pulse formaUon process indicated that balhst~c defect errors for the longer recoil track lengths increased sigmficantly w~th the shorter t~me constants 7) Therefore Gausstun shaping wtth a t~me constant of 4/~s was used for all spectrum measurements In nearly all cases this appeared to gwe the best experimental resolution The high voltage bins was set at 2300 V for the HE6 detector Thin corresponds to a gas mult~phcation of approximately 7 0 The high voltage bins for the HE20 detector was set at 3500 V These settings appeared optimum based on resolution constderatlons C~rcu~try to d~scnmmate against gamma-ray reduced events was not included m the electromc DETECTOR

SYSTEM PREAMP

m " I PULSER ] HIOH VOLTAOI~ (ORTEC 419) / IPOWER SUPPt-YI

,°12S2'o,o,

[

~'--I O0 IN'-) 2 S4CM F~g 1 Detector geometry

I(FLUKE 4008) I Fig 2 Electronic system

1

TIMING SINGLE I CHANNEL I ANALYSER I (ORTEC 420A)

I MULTI-

CHANNEL ANALYSER (TRACOR NORTHERN TN-170S)

T

511

AN ALPHA-RECOIL SPECTROMETER

,o'

"*•

H E 6 SA..ARAV RESPONSE

.

--0 OIISExt

v

io' (fJ I-Z :;;) 0 ¢.)

Io"

ETMAX " I

2,50 500 ENERGY IKEV)

I

750

Fag 3 HE6 gamma ray response

system The maximum energy that could be deposited by a gamma-ray induced event was cons~derably below the energy regmns of Interest for all detectors However, the intensity of gamma radlatmn near an operating reactor causes d~stortmns of the recod spectrum to occur at considerably higher energies than this maximum energy because of the pile up of gamma ray events in the processing system Therefore, a gamma ray background was simulated w~th a 6°Co source This source was placed close enough to each detector to produce a count rate equivalent to the gamma-ray background experienced during actual measurement cond~tmns A sample count rate d~strlbut~on is presented m fig 3 for the HE6 detector Above the theoretical maximum energy (Erm,x) that can be deposited by a single event, this distribution can be well approximated by an exponentml decay Based on this observation the lowest usable data bm in a recoil measurement can be calculated All of the recorded counts m the data bin closest to Ermax may be assumed to be gamma-ray reduced events Then the expected number of gamma-ray events can be calculated for all higher channels based on the determined exponentml relationship Gamma-ray perturbations of the recoil spectrum can be assumed neghglble when the expected statistical error m the recorded counts m a gwen energy bm is small This procedure is qmte conser-

vatlve but adequate for the energy ranges investigated with the alpha-recod spectrometer Pulse shape discnmmatlon should be possible in order to extend the energy range of thin detector to lower energies However the scattering cross section of helium falls off quite rapidly below 1 0 M e V Therefore, a proton-recod spectrometer would seem to be a much better choice for this energy range 3. Recoil response functions Recoil response functions for the alpha-recoil detector are very s~mllar to proton-recoil response functions The major difference is that hehum scatters amstroplcally in the center of mass system While the number of recoils generated per umt recoil energy is constant, from zero to the highest energy possible, for a neutron scattering off hydrogen, this is not the case for a neutron scattering off helium The number of recoils generated per unit recoil energy varies greatly from zero to the maximum possible energy for neutron-hehum reactions Above 4 to 5 MeV the scattenng ,s very predominantly in the forward direction for the reacting neutron A total of 6 Legendre components are required to adequately represent this forward-peaked scattering for energies below 20 MeV Recent ENDF-B updates estimate an accuracy of 2% for the neutron-4He scattering reactmn Thus, though the scattering response function ~s more comphcated, comparable accuracies should be attainable Within an lnfimtely large detector, the number of alpha-recoils generated per unit energy at recoil energy Er from a neutron flux density spectrum, ¢(E.), IS given by N~(Er) = VDNHe

E__.L 1-or

(1--0 0 g~ ×

(1) where

N~(Er) = the number of alpha recoils per unit energy at energy Er, gD NHe

O(E.)

the volume of the detector, = the number of 4He atoms per umt detector volume, = the neutron flux density per umt energy, neutrons/cm 2 s MeV, at energy E . , [(.4- 1)/(.4 + 1)12 and A ,s the mass of 4He in neutron mass units,

512

P J McDANIEL AND H E HUNGERFORD

#~

= the cosine of the angle of scattering for the neutron m the center of mass system It as umquely defined by the anltial neutron energy EN. and the final recoil energy Er, f (Eo) = the legendre components for the expansion of the 4He scattering reaction m the center of mass system, the scattering cross section per atom as (En) = for 4He at energy E . , = the pth Legendre polynomial of argument /le With a suitable redefinmon of terms this same equation applies to any elastic scattering reaction In fact for hydrogen, scattering (lsotroplc m the center of mass system) the fcp are all zero, yielding Np(Er) =

VoN.~ E~ as(E.)

q~(En) d e n

E. '

(2)

where Np(Er) as the number of recoil protons generated per unat energy This equation can be differentiated with respect to Er to gave the classic differential relationship for unfolding proton-recoil spectra ~'2) The measured spectra must be corrected for recoils that do not lose all of thear energy m the sensmve volume of the detector There are four categories of recoil tracks that can deposit energy in the sensitive volume of the detector 1) (1) tracks that start and stop within the sensmve volume, (2) tracks that start m the sensmve volume and pass out of at prior to stopping, (3) tracks that start outside of the sensmve volume and terminate within at, and (4) tracks that start outside of the sensmve volume, pass through it and termanate outside of it In this investigation only the first two categories were consadered The last two categories contain only a small fraction of the total number of tracks, and thear omission has not produced serious errors an the past In order to develop a quantitative measure of the response functions for the first two categories further simplifying assumptions are necessary If the neutron flux density is assumed to be constant across the dimensions of the detector, and if the charged-particle recoils are assumed to be generated isotropically w~thm the detector, a semi-analytic treatment is possible Both assumptsons have been evaluated for the measurement of reactor leakage spectra m a hydrogenous medium A worst case analysis shows that if the detector is not used to measure neutron spectra above the energy at

which 50% of all asotroplcally generated recoils terminate their tracks on the boundaries of the detector sensmve volume, the errors introduced by these assumptaons will be less than 10% at the highest energy measuredT), At the lower energies and for most reahstlc cases, the errors introduced by these assumptions wall be considerably less The fundamental relationship necessary to make thas wall-and-end effect correctaon, as the fractionof-recoil -tracks -not-truncated-by-the-detector-boundary vs recoil-energy relationship This can be labeled the F(Er) relatlonshlp It is derived from two other relationships The fraction-of-tracks-nottruncated vs recoil range relationship, P(R), and the recoil range vs recoil-energy relataonship, R(Er), must be calculated to obtain the F(Er) relationshap The P(R) relationship can be calculated by numerical quadrature The R(Er) relationship can be calculated for a given gas mixture from the data of Whahng 8) Then the F(Er) relationship can be obtained as F(Rr) = P ( R ( E r ) )

(3)

The relationship F(Er) Is necessary to calculate the first category of recoil events which deposit all of their energy within the detector The number of recoils that fall into the second category of events can be calculated based on the P(R) and R(E) relationships The number of recoils that deposat an energy Ed m the sensmve volume of the detector, prior to h m m g the wall or passing into the non-multiplying end zone, for a unit source of recoils at energy Er, as given by N(Ed)-

de(R) dR(E) , ~ R. ~ dE

(4)

where AE=E~-Ed, RT =R(Er)-R(,4E), the truncated track length within the detector Therefore the total number of recoils depositing an energy Ed m the detector is given by,

g(Ea) =

f(Ea) 6(Ed-E~) -d

dP(R) R. dR(E) } N(Er) dEr, dR dE dE

(5/

where 8(Ea-E~) Is the Dlrac delta function and all of the other terms retain their previous definitions This integral transformation must be applied to the mfimte detector recoil spectrum m order to correct for the fimte size of the detector

513

AN A L P H A - R E C O I L S P E C T R O M E T E R

In addition to the primary scattering nuchde, a number of other nuclides are present in the detectors These include krypton, carbon, oxygen, nitrogen and 3He Of these only carbon, oxygen and nitrogen recoils need be considered The recoil response function for these materials is similar to the helium lnfimte detector response The lower energies and shorter ranges involved with scattermg from krypton do not require a finite detector correction 3He is a very minor component, and its scattering properties are not sufficiently different from those of 4He to slgmficantly influence the results Finally, if the alpha-recoil detector is to be coupled to a proton-recoil detector It is advantageous to transform the independent variable used to represent the neutron flux density spectrum from E. to l n E . ( = 0.) Making this transformation, the final integral equation representing the spectrum measurement Is given by, C(V,)

=

NH¢ Vd

Ed(V,)

F(E,) (Er-Ed) --

dP(RT) dR(AE) 1 dR ~ - _ix

fj

~

as(V.) e - "

o~ ~IE~_~~ (1-~)

x

[I+v=xL ( 2 p + l ) fcp(v.)Pp(p¢)]× X

~(Vn) dv.dE, ×

X

Vd

X

X

,=1

[°

N,~t

og~

~s (Vr,) e-V. (1 - ~ ) ×

p=l

¢(%) dr.,

x

(6)

where

c(v,)

=[(A - 1)/(.4 + 1)]2 and A is the mass of the /th secondary scatterer in neutrons mass units, = the pth Legendre expansion component for the ith secondary scatterer's scatterl n g c r o s s section, and where the other variables have already been defined 4. Unfolding procedure Eq (6) may be solved for the unknown neutron spectrum, e(V.), by making the continuous equation a discrete function in some manner, and then inverting resulting matrix This conversion is quite easily accomplished if the following substitution is made N

~b(v.) = ~ X~ Sy(%)

(7)

.1=1

The X~ are a set of coefficients for the basis functions, SK(O.) There are many possible sets of basis functions, a particularly convenient set are the B-sphnes In fact there are an infinite number of orders of Bsphnes, but in this study only the first few orders have been considered The B-sphnes have many properties that make them attractive basis functions for this type of problem 9) The first four orders of B-sphnes are described m fig 4 A set of B-sphnes of order K are defined by a constant shape function made up of pieces of a low Kth-order polynomial that IS shifted by a constant mesh spacing H along the independent variable axis to define each new basis function The mesh interval is defined by n = @max--Vm,.)/(N-- K),

1}

1+ 2 ( 2 p + l ) :~,¢t, " (v.) Pp(P~)

O~ss~

the recorded counts at voltage V, for the tth bin of the multi-channel analyzer, E,~(V,) = the detected energy corresponding to the voltage V,, F(Er) = the fraction of non-truncated tracks at energy Er, e(o.) = the neutron flux density per unit o . ( = l n E . ) In the detector, the number of atoms per cubic cenNsst timeter for the /th secondary scatterer,

(8)

where Omaxand Ore,. are the limits of the independent variable, N is the number of basis functions, and K is the order of sphne As an example, the second member of the set of first order sphnes would be defined by S k(v) = v/H ,

O <_v < H ,

S ½(v) = 1 O - ( v - H ) / n ,

H< v<2H

(9)

Though the B-spllnes are not m general orthogohal, they can be manipulated quite easily on a digital computer Substitution of eq (7) into eq (6) and numerical integration of the detector response times the expansion for e(o.) from or.,. to o.,ax converts the set

514

1, J

-~

AND H

×

A

FIRST ORDER

'°l

S'

X

SECOND ORDER

'°l

S~

)

I

H

I

,

X

,°l

S3

i

~

THIRD ORDER ,

'

Fig 4 T h e first four B - s p h n e s

of integral equations for each bm of the accumulated spectrum into a set of &screte equations in the X~ expansion coefficients If each equation Is weighted w~th the reciprocal of the expected error m ~ts measured data value, then this set of equations can be represented m matrix form as A X = B, or _C,___,

K,j X j = 1

et

d

e,

for

, = 1,2,

,M,

(10)

where M = the number of bins of data m the measured recoil spectrum, K U = the integral of the detector response for the ah bin over the kth basis function, e, = the expected error m the tth equation The unfolding problem has now been reduced to solwng for the X vector by reverting the A matrix In general this is an unstable process The method used here follows the work of Hanson and Lawson~°), and a number of their routines were used m the computer ~mplementat~on The reversion can be accomphshed by factoring A into three matrices Two of these (U, Vr) are umt orthogonal and one (S) is dmgonal AX = Ysv Tx = B

E

HUNGERFORD

The superscnpt T denotes the transposed matrix Then s v T x = U'r B (12)

ZERO ORDER

So

°t

McDANIEL

(11)

The mstabllmes in solwng for X arise from small elements of the S matnx Small elements of S produce large elements m S reverse (S-t), as the elements of S-1 are the reciprocals of S Therefore a stable solution for X can be obtained by hm~ting the minimum s~ze of an element in S. Th~s can be accomphshed based on the error m the original set of data For a set of M equations used to determine N parameters w~th a unit variance m the expected error m each equation, the sum of the squares of errors m the set of equations will have an expected value of M - N , based on chl-square statistics The sum of the squares of the elements in the S matrix is equal to the sum of the squares of the errors m the ongmal set of equations For typical unfolding problems thin sum ~s qmte a b~t less than its expected value Therefore the problem may be stablhzed by increasing this sum of squared errors This may be accomphshed by perturbmg the S matrix so as to entirely remove the smaller elements or to hm~t the minimum s~ze that an element can attain Either procedure can be used to increase the squared error m the set of equations until it ms equal to Its expected value 7) Then defining the new matrix as s, the matrix mversion can be completed to gwe X = V $ -1 U T B (13) This process ~s stable and has produced rehable resuits Addmonal mformat~on such as boundary condmons and non-negatw~ty constraints may be incorporated into the solution 7) As a test of the procedure and computer codes developed to analyze the alpha-recoil spectrometer data a sample computer problem was attempted A theoretical spectrum for a plutonmm-berylhum - - - THEORY-VD Z --

UNFOLDED

-

I°/o

ERROR t

I 3

Ftg 5 Test case

l 4 E N ERGY

(MEV)

/,

I

I

I

5

6

7

•

9

10

AN ALPHA-RECOIL SPECTROMETER source was obtained from Van der Zwan's calculations ]~) This curve was converted to a In E scale and used as a sample spectrum The expected recod spectrum for the HE20 detector was calculated for th~s neutron spectrum Th~s recod spectrum was then perturbed w~th random errors to simulate data errors The distribution of errors was assumed normal wtth a standard devmtion equal to 196 of each data value This calculated spectrum was then unfolded as ff ~t were real data The resuits are presented m fig 5 The estimated errors returned for the unfolded spectrum are approx;mately 3 to 4% of the unfolded values Clearly, if an accurate response matrix ~s generated and data errors can be kept to the 196 level, the alpha-recoil spectrum can be unfolded

5. Experimental results A number of spectra were measured w~th the alpha-recod spectrometer As a test of the calculated response matrix, two neutron sources of relatively well known structure were measured As a test of the couphng procedures for combining alpha-recoil data w~th proton-recod data the leakage spectrum from the PUR-1 pool reactor was measured w~th the HE6 and H10 detectors A one-curie plutonmm-berylhum source was measured w~th the HE20 detector The source was placed on a table approximately one inch from the s~de of the detector and counted for about 4 days The resulting spectrum is presented against Van der Zwan's calculation m fig 6 There are slgmficant d~fferences, though characteristic peaks are ~dent~fied at 3 3, 4 5, 6 6 and 9 6 MeV. There is an extraneous peak at 3 7 MeV, and the large peak expected at 7 7 MeV ~s m~ssmg There ~s also a large hump at 5 8-6 2 MeV Closer analysm of the detector gas composition revealed that nitrogen has a qmte large (n, 0:) reaction cross section m th~s energy range, approaching 0 5 b In fact a peak m ....

r.~oav VDZ MEASUREMENT

HE20 //.x\

/

x

iI

~k I

ENERGY

(MEV)

Fig 6 Plutomum-berylhum spectrum

l

'~ ~

515

--- T.EORY-VDZ

I

uJ

\ ENEPqY

4 (MEV)

5

6

7

8

9

I0

Ftg 7 Amencmm-berylhumspectrum the mtrogen cross section at 2 55 MeV corresponds to the extraneous peak at 3 7 MeV The broad hump around 6 0 MeV also corresponds to structure m the mtrogen cross secUon An attempt was made to include this reaction in the unfolding process It was not very successful, presumably because of a lack of accurate knowledge of the nitrogen cross section However, when th~s reaction was included, a peak m the unfolded spectrum did appear at 7 7 MeV The efficiency of the HE6 detector was less than one third of the efficiency of the HE20 detector Therefore, a larger source was necessary to obtain adequate staUstlcs in a reasonable amount of time with ~t An amer~cmm-berylhum source at Argonne National Laboratory w~th a strength of approximately eight curies was made avadable Thin source was measured w~th the HE6 detector at a distance of approximately one inch The recod spectrum was accumulated for about 50 h The unfolded results are presented m fig 7 and are compared with a calculated spectrum also due to Van der Zwan The peaks at 96, 7 9 and 4 9 MeV are obvious Because of the large source used there ~s enough w~thm-the-source scattering that the peak at 4 9 MeV and lower energy portions of the spectrum are increased m magmtude compared to the high energy peaks Also, a fission peak shows up at about 2 1 MeV The loss of the peak at 3 3 MeV is not completely explainable There ~s a shght rise m the unfolded spectrum at this point and possibly this is all that is left of this peak after ~t has been smeared w~th the poorer resolution of the detector m th~s energy range It ~s also possible that the peak ~s m actuahty not qmte as prominent as the calculated curve mdmcates Finally, the reactor leakage spectrum from the PUR-1 reactor was measured The PUR-1 reactor

516

P J McDANiEL AND H E HUNGERFORD

FISSION

~1O"

SPECTRUM

~

\\\\\

i

; oz5

:

: o5

I

; : ;; ,o

ENEROY

I

I

t

I

2

3

4

5

! s7

I

I s

(MEV)

Fig 8 PUR-1 leakage spectrum

is a small, low-power (1 kW) swlmmmgpool type reactor with uramum-alummum sandwich fuel plates. The core region is a rectangular paralleleliplped with a base, 30 by 30 cm, and a height of approximately 60 cm It is surrounded on the sides by a 7 56 cm thick reflector made of graphite A 5 0 cm thick lead shield was placed against the front face of the reactor for this measurement The detectors were placed m the water centered on the front face of the reactor at approximately 5 cm from the lead shield A measurement of the neutron leakage flux density was made with the HE6 and H10 detectors The unfolded results of that measurement are presented m fig 8 A number of the features of the spectrum are readily explainable The dip at approximately 0 4 MeV corresponds to a peak m the oxygen cross section The dip at 2 0 MeV and peak at 2.5 MeV also correspond to structure m the oxygen cross section The peak before and dip after, 3 0 MeV correspond to a resonance in carbon and are the results of leakage through the graphite reflector The peak at 4 0 MeV corresponds to a dip m the oxygen cross section The peak above 7.0 MeV corresponds to a dip m the carbon reflector cross section The overall decrease in the spectrum above 1 0 to 2 0 MeV corresponds partly to an increase m the inelastic scattering cross section

for the lead The relative errors for this spectrum are a bit larger than for other spectra with similar counting statistics, as the errors due to relative reactor power levels and detector placement have been included

6. Conclusions The alpha-recoil spectrometer does work and can provide reasonable resolution in the energy range from 1 0 to 10 0 MeV Errors m the generation of the response matrix can have a disastrous effect on the unfolded results Therefore the quantity of secondary scatterers that ms included m the detector should be kept to the absolute minimum necessary A more nearly optimum detector gas composition would appear to be 25 atm of helium, 5 atm of krypton, and 1 atm carbon-dioxide with enough 3He to calibrate This mixture should require a high voltage around 4500 V and provide a reasonable response up to 11 5 MeV References 1) E F Bennett and T J Yule, Techmques and analysts of fast reactor neutron spectroscopy wtth proton-recod proporttonal counters, ANL 7763, Argonne, IL (August 1971) 2) p W BenJamin, C D Kemshali and J Redfearn, Nucl Instr and Meth 59 (1968) 77 3) W R Burrus and V V Verblnskl, Nucl Instr and Meth 67 (1969) 181 4) M G Silk, J Nucl Energy 22 (1968) 163 5) C D Lwengood, Development of a fast neutron spectrometer and measurement of neutron spectra transmttted through tron slabs, Ph D Thesis submitted to the Nuclear Engmeenng Department of Purdue Unlv (August 1970) 6) j M Larson, A rode-band charge-senstttve preamphfier for proton-recod proporttonal countmg, ANL 7517, Argonne, IL (February 1969) 7) p j McDamel, An alpha-recod spectrometer, Ph D Thesis submitted to the Nuclear Engmeenng Department of Purdue Unlv (May 1977) s) W Whaling, The energy loss of charged partwles m matter, Encyclopedia of physics, vol 34 (Spnnger-Verlag, Berhn, 1958) 9) p M Prenter, Sphnes and vanattonal methods (John Wdey, New York, 1975) ]o) R J Hanson and C L Lawson, Solving least squares problems (Prentice-Hall, Englewood Cliffs, 1974) H) L van der Zwan and K W Gelger, Nucl Instr and Meth 131 (1975) 315