APPENDIX 2

Simulation of the T(d,y)5He Pulse Height Spectrum

To simulate the pulse height spectrum of gamma rays to the unbound ground state and first excited state of 5He, it was necessary to assume theoretical lineshapes for the two decays. A convenient representation of the spectral shapes was used which was analogous to one in the analysis of the mirror reaction (King et~· 1972, and references therein):

where G(E )

y is the(theoretical) gamma intensity at energy E

S is the resonant n +a phase shift ;

P is the Breit-Wigner penetrability for ~

=

1 (Preston 1962' p. 51 7) ;

a is the transition strength ;

subscript O is the transition to 3/2 ground state ; and subscript 1 is the transition to 1/2 first excited state.

The factor E3 arises from an assumption of El transitions. The reson-

ant phase shifts were computed from literature values of the n + a scattering phase shifts (Arndt and Roper 1973), assuming that the hard sphere phase shift corresponds to a radius of 2.5 fm. The resonant phase shift S~ is defined as follows (Lane and Thomas, pp. 269-281):

where ₆_Q, is the tot a 1 phase shift

- cp

Q, is the hard sphere phase shift and

WQ, is the Coulomb phase shift = O for neutrons.

The actual photon spectrum GE and the pulse height spectrum produced by the detector NK are related by:

. '

where EE is the detection efficiency of Na I crystal and boron- paraffi n attenuation at energy E (see page 22 ); and AE,K is the probability that photon of energy E is assiqned

a channel K by the multichannel analyzer connected to the detector.

The detector response function for a monoenergetic y-ray of energy E was parameterized as follows (King et~· and references therein):

AE,K

=

a₀ + a1 exp[a2(K-E)]

AE,K

=

a3 exp[-a4(K-E)2

J

K < E

K > E

where a

0, a1, a2, a3, a4 are empirical, energy-dependent parameters. The parameters used here were determined by a nonlinear, least-squares fit to monoenergetic gamma spectra from the reactions T(d,y) 4He anrl 11B(d,ny

15.1)12

c,

the standard spectra were accumulated at identical experimental conditions (such as target-to-detector distance, attenuator

and collimation) as the T(d,y) reaction. Figure 4 shows a typical T(p,y) lineshape and the fit using the analytic form above. A hori- zontal extrapolation of the lineshape to zero energy was assumed. The exact form of the lineshape in the low pulse height region is not

known, and this introduces an uncertainty in the absolute cross section of about 10%. The lineshape fitting was carried out with the computer code NAIPK which is based on the program CURFIT given by Bevington

(1969, p. 237).

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T. W.Donnelly 1967, Ph.D. Thesis, University of British Columbia.

P. L. Dyer 1973, Ph.D. Thesis, California Institute of Technology.

A. Fassler 1965, Nuc. Phys. §.§_, 329.

A. J. Ferguson 1965, Angular Correlation Methods in Gamma-Ray Spectros-

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P. Heiss and H. Hackenbroich 1971, Nuc. Phys. Al62, 530.

P. E. Hodgson 1963, The 0 tical Model of Elastic Scattering (Oxford University Press, Amen House, London EC4 .

P. E. Hodgson 1967, Ann. Rev. Nuc. Science

l.Z.,

P. E. Hodgson 1971, Nuclear Reactions and Nuclear Structure (Clarendon Press, Oxford .

B. Hoop Jr. and H. Barschall 1966, Nuc. Phys. 83, 65.

H. T. King, W. E. Meyerhof and R. G. Hirko 1972, Nuc. Phys. Al78, 337.

A. Kosiara and H. B. Willard 1970, Phys. Lett. 328, 99.

A. M. Lane and R. G. Thomas 1958, Rev. Mod. Phys. 30, 257.

J. D. Larson 1965, Ph.D. Thesis, California Institute of Technology.

N. H. Lazar, R. C. Davis and P. R. Bell 1956, Nucleonics .!i_, 52.

E. B. Lyovshin et

tl·

1974, Phys. Lett. 528, 392.

J. B. Marion and J. L. Fowler 1960, Fast Neutron Physics, Part I (Inter- science, New York).

J. B. Marion and F. C. Young 1968, Nuclear Reaction Analysis (North- Holland, Amsterdam).

M. A. Melkanoff, D.

A FORTRAN Pro pt1cal Moe Angeles).

S. Saxon, J. S. Nodvik and D. G. Cantor 1961,

ram for Elastic Scattering Analyses with the Nuclear

M. A. Melkanoff, T. Sawada and J. Raynal 1966 in Methods in Computational Physics, Vol. 6, Nuclear Physics, ed. by B. Alder,

S.

Fernbach, and M. Rotenberg (Academic Press).

W. E. Meyerhof, M. Suffert and

W.

Feldman 1970, Nuc. Phys. Al48, 211.

P.D.M. Parker 1963, Ph.D. Thesis, California Institute of Technology.

J. D. Pearson 1963, Ph.D. Thesis, California Institute of Technology.

C. M. Perey and F. G. Perey 1972, Nuclear Data Tables lQ_, 539.

C. M. Perey and F. G. Perey 1974, Atomic Data and Nuclear Data Tables _ll, 293.

J. E. Perry, Jr. and S. J. Bame 1955, Phys. Rev. 99' 1368.

J. Polchinski 1974, Private communication.

J. Polchinski 1975' Private communication.

M. A. Preston 1962, Ph~s i cs of the Nucleus (Addison-Wesley, Massachusetts) M. Radomski 1975, Private communication.

C. Rolfs 1973, Nuc. Phys. A217, 29.

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M. E. Rose 1953, Phys. Rev. 21_, 610.

G. Satchler et _tl. 1968, Nuc. Phys. Al12, 1.

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115.

TABLE l

Detection Efficiency for 8¹¹x5¹¹ Na.I (T,!) at 31¹¹ from Target (see text, p.21)

Absorbing medium: paraffin +

s

₂

o

₃cone (29¹¹⁾ glass wall - 3/16¹¹

E y

19.0 24.9

l /l 6¹¹ lead

Steel housing and Al

o

₃around crystal dS1/4TI

=

0.4 X 10 -2

Jn - 2TI

f

Pn(cos e)

-µ i (l - e 2 2

) dS"t

crystal attenuation detection in NaI in absorbing

medium attenuation factors Qn

=

Jn/J

Detection Efficiency -µlxl e

E:: J/2 Ql Q2 attenuation in cone 0.8xl0- 3 .996 .989 0.27 0.9xl0 -3 .996 .989 0.29

l - e -µ2X2 detection

in NaI 0.86 0. 88

TABLE 2

Attenuation of 19.5 MeV Y-Rays in the Material between Target and NaI Detector - See text, p. 22.

MATERIAL

paraffin +

s

₂

o

₃

glass lead sheet

stainless steel housing of crystal

Al2

o

₃reflector of the crystal

target and target backing

*

_at

e =

0° runs only.

LENGTH

29¹¹ 3/16¹¹ l /l 6¹¹ 0.019¹¹

1/16¹¹ (67 mg/cm2 ) 3 mg/cm2

Zr 10 mil Pt 1/8¹¹ Cu

TRANSMISSION (e-]JX)

0.31 0.98 0.89 0.99

0.99 0.90

*

E y

(MeV)

24.22 23. 1 22.74 21. 99 20.88 15 .11

TABLE 3

Measurements of the Spectrum Fraction for Monochromatic y-Rays. See text, p. 22.

Spectrum Fraction

( 0 • 8 E o to 1 • 1 E ⁰)

y y

0.42 0.40 0.40 0.42 0.39 0.38

El ab d (MeV)

2 6 12

TABLE 4

Simulation of Pulse Height Spectrum for T(d,y) ⁵He See text, p. 22 and Appendix 2.

E y

(MeV) 17 .8 20.2 23.7

Only Transitions to Ground State

(spectrum) fraction

0.40 0.38 0.38

FWHM

48%

44%

41%

Equal Amplitudes for Tran- sitions to Ground State and First Excited State

f FWHM

0.38 74%

0.37 71%

0.39 66%

El ab

d (MeV)

4 8 10 12

TABLE 5

Results of Fits to Angular Distribution See text, p. 2 6.

E(He5 ) (MeV)

19.0

21.4 22.6 23.8

Fit with A

0 +Al 2 A2/Ao

-.03 ^± .07 -.20 ^± .07 -.30 ± .07 -.44 ± .06

Fit with Ao+A1P1+A2P2

A2/Ao Al/Ao

. 02 ± • 10 - . 07 ± • 10

-.13 ± .08 - . l 0 ^± ^•08 -. 26 ± .10 - . 05 ± • 10

-.34 ^± .06 -.11 ^± .06

Table 6

Parameter Sensitivity of Total Direct Capture Calculation of T(d,yE

1)5Heg.s. (See text, p. 69 )

Parameter Original value

Variation in Parameter limit on radial integration and mesh size:

rmax 15 fm 20 fm

cS r 0.025 fm 0.010 fm

initial-state po ten ti al parameters [in e9 ~

R c ^l.3 * 3 l /3 _± 10%

Vi 45.0 ^± 10%

;f

dE 0.124 ^± 10%

(energy dependence)

RV l.75*3113 ± 10%

av 0.593 ^± 10%

w 0.610 ^± 10%

dW/dE 0.056 ^± 10%

RW 4.458* 3l/ 3 ^± 10%

dRw/dE -0. 165 * 3113 _± 10%

aw 0.526 ^± 10%

( 1 ) '

final-state potential parameters [in eq. (2) ² _~-

RC l.3* 31/3 _±10%

RV l. 75 * 3l13 ± 10%

a v 0.593 ^± 10%

Q 16.7 ^± 10%

Maximum Variation in Calculated Cross Section

< 1%

< l % p. 56]:

20%

factor of 4 3%

factor of 8 20%

10%

59]:

20%

35%

25%

50%

Figure 1

Energy Level Diagram of the 5He and 5Li Nuclei (Ajzenberg- Selove and Lauritsen 1974), see text, p. 1 and p. 41.

""Tl -'· u:i c: ~ Cl) ._.

1~21.aJ

I r---

SH

-2.1 I 3H+2n

t

IMEV

T

19.85 3 He+2n 18.92 2

9?9T»h?~¥t

3H+p+n 18.61

I

17. ,,~,, 1112'1, 16.7016.77 312+1 3H+ 2 77

r/#~nn

He+n+p 3H+ d ---

!

16.66 312+ 16.39 -0.89 4 He+ n 5

He

Li

3 He+d -1.97 4 He +p

I I I I

lt>_go.~_ - --l

Be l

I I I 1-4.2 3 He+2p I \.0

°'

Fi gure 2

Schematic Diagram of the Target and Detection System

The leftdiagram shows a vertical section of the target chamber and vacuum system (not to scale). For additional details, see p. 10.

The right diagram shows the detector geometry and the lead shielding (not to scale). For additional details, see p. 11.

LIQUID NITROGEN COLLIMATOR COLO TRAP ION PUMP

~ t-1

BEAMDIRECTKlN_.

! t1 I I~ /

BEAM TUBE TARGET GLASS-T LEAD SHIELDING Nol (Tl) CRYSTAL

Figure 3

Electronic Configuration for Measurements of T(d,y)5He and T(p,y)5He Yields. See text, p. 12.

a"

x 511 Nol {Tl) RCA 4522 j DYNODE 9 I PREAMPLIFIER

~I

LINEAR DELAY

r-1

AMPLIFIER

~I-

X ADC

I

,,

... FAST (.Q TIME- c: 11 START11 -s ANODE DISCRIMINATOR TO- Cl) I> ~I w (low level AMPLITUDE Y ADC timing) CONVERTER

?

"s/op"

LINEAR

I r1

FAST I> AMPLIFIER ANTENNA DELAY DISCRIMINATOR AT CHOPPER

Figure 4

21 MeV Standard Spectrum for an 8¹¹ x 5¹¹ Na I (T.Q.) Crystal

This pulse height spectrum for a monochromatic y-ray was meas- ured with the T(p,y) 4He reaction (Q

=

19.8 MeV) at E~ab

=

^{1.5 MeV.}

The dots represent the data with the background subtracted. The solid line represents the nonlinear least-squares fit described in Appendix 2. The dashed line represents an estimate of the low energy background. See text, p. lb and Appendix 2.

w

z z

500

250 ~

Cf)

~ ²⁰⁰

::::>

u 150

..,

I

I I I I ~

I I

I

L, I

I

• L, •

.,

FIT TO y-RAY PULSE HEIGHT SPECTRUM

T (p,y) ⁴He

E~b = 1.5 MeV, 8₁ab =90°

IOOL---~-1-::-.IA-:'---

L • •••

50 0 0

~ _....,

• L..,

... ..._

• __________

^__..~

..

32

Dalam dokumen A STUDY OF THE T(d,y)5He REACTION - CORE (Halaman 88-108)

=

. '

=

=

J

c,