STATISTICAL-MODEL CALCULATION OF THE SELECTIVE EXCITATION OF HIGH-SPIN STATES IN 24Mg

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STATISTICAL-MODEL CALCULATION OF THE SELECTIVE EXCITATION OF HIGH-SPIN STATES

IN 24Mg

R. Malmin, K. Katori, L. Greenwood, T. Braid, R. Siemssen

To cite this version:

R. Malmin, K. Katori, L. Greenwood, T. Braid, R. Siemssen. STATISTICAL-MODEL CALCULA-

TION OF THE SELECTIVE EXCITATION OF HIGH-SPIN STATES IN 24Mg. Journal de Physique

Colloques, 1971, 32 (C6), pp.C6-223-C6-224. �10.1051/jphyscol:1971649�. �jpa-00214867�

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JOURNAL DE PHYSIQUE

Colloque C6, supplkment au no 11-12, Tome 32, Novembre-Dkcembre 1971, page C6-223

STATISTICAL-MODEL CALCULATION

OF THE SELECTIVE EXCITATION OF HIGH-SPIN STATES IN 24Mg (*)

R. E. MALMIN, K. KATORI, L. R. GREENWOOD, T. H. BRAID and R. H. SIEMSSEN Argonne National Laboratory, USA

R6surnB.

-

Le peuplement selectif d'ktats de haut spin dans le

^24Mg

par la rkaction

l z C ( 1 6 0 , u)24Mg,

de mCme que I'absence d'une telle sklectivite dans la rkaction

^14N(14N,a ) z 4 M g

peuvent Ctre expliques par des calculs faits dans le cadre du modele statistique de Hauser-Feshbach.

Abstract.

-

The selective population of high-spin states in

^{2 4 M g}

by

12C(160, u)24Mg

reaction, as well as the lack of such selectivity in the

^14N(14N,a)24Mg

reaction, can be explained in terms of a Hauser-Feshbach statistical-model calculation.

In the '2C(160, ~ t ) ' ~ M g * reaction, several states in 24Mg a t -- 16 MeV excitation were found to be selec- tively and strongly populated [I]. In contrast, the 1 4 ~ ( 1 4 N , a)24Mg* reaction exhibits a n evaporation spectrum which is smooth and without prominent peaks [2]. The differences between the two reactions as well as the strong and selective population of states in the '2C(160, reaction can readily be explained with the statistical model if the prominent states in 24Mg have high spin, a n assumption which indeed has been confirmed for all states whose spins have been determined [3], [4]. The measured excitation functions of the 12C(160, ~x)'~Mg reaction show strong fluctuations [5] and therefore indicate a strong compound nuclear component in the cross section.

In figure 1, grazing angular momenta Ll12 for

5 10 15 2 0

E E X C ( M e V )

FIG. 1. -

Grazing angular momenta

,5112

for various reaction channels leading to the compound nucleus

28Si

at

38.2

MeV excitation. The abscissa is the excitation energy

in

the reaction

channels.

(*)

Work performed under the auspices of the

U.

S . Atomic Energy Commission.

various reaction channels leading to the compound nucleus 28Si* a t 38.2 MeV excitation are plotted versus excitation energy in the reaction channels. The 28Si*

energy of 38.2 MeV corresponds to a n incident energy of E,,, = 50 MeV in the "C +

¹⁶⁰

system.

Considerably higher angular momenta can be carried into 28Si via l z C + 160 (Ll12 = 16 h) than via 14N + I4N (L1,'

=

7 A). Since there are only very few open channels that can carry away the largest angular momenta brought into the system by 12C + 160, one will expect C N reactions t o feed these channels strongly. In contrast, even the highest spin states excited by the 14N + 14N reaction can a decay to all spin states in 24Mg for Ex 5 20 MeV.

Therefore one does not expect a selective population of high-spin states in the 1 4 ~ ( 1 4 N , a)24Mg reaction.

We have used the Hauser-Feshbach theory to calcu- late the population of states in 24Mg. The familiar expression for the total cross section is

We have calculated the denominator G ( J ) as a discrete sum over all known levels in nine reaction channels plus a n integral over the continuum region using a standard level density expression [6]. Optical- model transmission coefficients were calculated a t a number of energies and were fitted a s a function of energy and I with a 3-parameter Fermi function with energy-dependent parameters. Transmission coeffi- cients generated by this procedure agreed with the original optical model transmission coefficients t o

- ¹⁰ ^% for all important channels. The present calculations neglect direct reactions and assume that the absorption given by the transmission coefficients T , is due t o CN processes only. The calculated cross

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971649

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C6-224 R. E. MALMIN, K. KATORI, L. R. GREENWOOD, T. H. BRAID AND R. H. SIEMSSEN sections are therefore upper limits for t h e C N contri-

bution.

Figure 2 shows a plot of G(J) a l o n g with contribu- tions t o G(J) from

1 2

C +

1 6

0 ,

2 4

M g + a, a n d

1 4

N +

1 4

N channels. F o r large values of / , t h e deno- m i n a t o r is d o m i n a t e d by t h e

1 2

C +

1 6

0 entrance channel a n d high-spin states of the

2 4

M g + a channel a n d is very sensitive t o t h e n u m b e r a n d excitation

FIG. 2. — « Number of open channels » G(J) for the decay of the compound nucleus

28

Si at 38.2 MeV for different compound- nucleus spins / . The total contributions from the

12

C +

1 6

0 ,

14

N + i4N, and

24

Mg + a channels to G(J) are also shown.

energy"~of high-spin states in

2 4

M g . Uncertainties in the level-density parameters m a k e some quantitative differences in t h e results obtained (which a r e strongly dependent on t h e behavior a t high / ) , but the qualita- tive results for

1 2

C +

1 6

0 a n d

1 4

N +

1 4

N reactions remain unchanged.

Figure 3 is a plot of cross sections t o various / *

states a t 12-18 M e V excitation energy in

2 4

M g The left-hand ordinate is total cross section a n d (if a 1/sin 0 angular distribution is assumed) t h e right- h a n d ordinate corresponds t o differential cross sec- tion a t 0

o m <

= 12°. Absolute cross sections a r e consistent with experiment. A s can b e seen from this figure, states of I

f

= 6-10 are very strongly populated relative t o states of lower spin in t h e

1 2

C +

1 6

0 reaction, in m a r k e d contrast t o the

1 4

N +

1 4

N results.

0.001 U 1 I I i L 12 15 18 12 15 18

E (Z 4Mg), MeV

FIG. 3. — Cross sections for the population of natural-parity states in

24

Mg for excitation energies between 12 and 18 MeV.

Using a (I = 0-5) from figure 3 as a background a n d employing level-density parameters t o find the n u m b e r of levels in a 16-17 MeV region of excitation in

2 4

M g leads t o estimated peak-to-background ratios whose values for / = 10, 9, 8, 7 a n d 6 are respectively, 1 1 , 6, 3 , 2 a n d 1 for

1 2

C (

i e

O , a )

2 4

M g a n d 0.38, 0.26, 0.19, 0.14 a n d 0.1 for

1 4

N (

1 4

N , a )

2 4

M g , in qualitative agreement with experimentally observed spectra.

References

[1] MIDDLETON (R.), GARRETT (J. D.) and FORTUNE (H. T.),

Phys. Rev. Letters, 1970, 24, 1436.

[2] MIDDLETON (R.), GARRETT (J. D.) and FORTUNE (H. T.),

Bull. Am. Phys. Soc., 1971, 16, 37 and preprint.

[3] GOBBI (A.) et at, Phys. Rev. Letters, 1971, 26, 396.

[4] BALAMUTH (D. P.), HOLDEN (J. E.), N O E (J. W.) and

ZURMUHLE (R. W.), Phys. Rev. Letters, 1971, 26, 1271.

[5] GREENWOOD (L. R.), BRAID (T. H.), KATORI (K.), STOLTZFUS (J. C.) and SIEMSSEN (R. H.), Bull.

Am. Phys. Soc, 1971, 16, 37 and contribution to this Conference.

[6] FACCHINI (U.), SAETTA-MENICHELLA (E.), Energia