Carla: A code to calculate the population of high spin states through compound nucleus reactions

Carla: A code to calculate the population of high spin states through compound nucleus reactions

Computer Physics Communications 15 (1978) 283—290 © North-Holland Publishing Company CARLA: A CODE TO CALCULATE THE POPULATION OF HIGH SPIN STATES TH...

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Computer Physics Communications 15 (1978) 283—290 © North-Holland Publishing Company

CARLA: A CODE TO CALCULATE THE POPULATION OF HIGH SPIN STATES THROUGH COMPOUND NUCLEUS REACTIONS C. SAVELLI and M. MORANDO Istituto di Fisica and INFN, Padova, Italy Received 8 August 1977; in revised form 10 April 1978

PROGRAM SUMMARY Title of program: CARLA

Card punching code: BCD

Catalogue number: ABGQ

Keywords: Nuclear physics, reaction, compound nucleus, Hauser—Feshbach, level density, yrast level, high spin state

Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Computer: CDC 7600; Installation: Centro di Calcolo Interuniversitario deil’Italia Nord-Orientale, Bologna Operating system: SCOPE 2.1.3.

Nature of physical problem Calculation of the direct population of high spin state in the frame of statistical model. Method of solution The absolute cross section was calculated evaluating the integrals with the first order Gauss-Legendre method.

Programming language used: FORTRAN IV High speed storage required: 25320 words No. of bits in a word: 60 Overlay structure: none No. of magnetic tapes required: none

Restrictions on program complexity Emission of a maximum of 3 particles of the type n,p,~(the formula used is repetitive, but for more than 3 particles the calculation increases greatly). The population of 10 levels by seven different beam energies may be obtained at one time. Typical running time This time is strongly dependent on the required calculations.

Other peripherals used: card reader, line printer, disc No. of cards in combined program and test deck: 1085

Unusual feature of the program The program calculates the direct population of level.

C. Savelli and M. Morando / Population of high spin states

284

LONG WRITE-UP 1. PhysicaL aspect

level, and N the number of evaporated light particles.

The main goal of the present code is to investigate the strong selective population of a nucleus reached through the evaporation of light particles in heavy ion induced reactions as experimental data indicate

The cross section for direct population of this level is given by [9] ~ E~,J*)

[1]; it calculates the cross section for direct population of levels of residual nuclei in reactions of the typeA(a,xcs+yp+zn)B. The main physical assumptions in the code are: a) Only the compound nucleus mechanism contributes to the reaction. No corrections to the extreme model are made. b) The compound nuclear state is formed in the continuum region of parameters the spectrum. Its spin distribution depends on the of the entrance channel. c) This compound state decays to the yrast states of the residual nucleus through successive emission of light particles; only alpha, neutron and proton particles are considered, no gamma-decay is taken into account at this stage. d) The intermediate states are also compound nuclear states in the region of strong overlapping levels. e) All the effects of angular momentum conservation are taken into account; the parity is neglected. These assumptions allow the process to be described by the statistical spin-dependent theory of Hauser and Feshbach [2]. There are other codes that make calculations of the same type, but many of these calculate only the total cross-section for light ions induced reaction [3,4], others [3,4,5] consider HI induced reaction, but few of these [6] take into account a complete and correct treatment of all angular momentum effects. At present the code can handle the evaporation of a maximum of three particles; it has been used with success [7] around the mass A = 50. Satisfactory results were obtained even for light ion induced reaction in the same mass region [8]. 2. FormuLas and parameters

(~ N-i

1

~

=

01

PK&2,~+l\~N

~

~

D

~

where the integral is calculated from E* toEs IQ~Jand

)

(1)

~‘

N1 + ~



01 Ea

1(E1,Jj) +



2

(21+l)(2i+1)

fiX

T 1o 10(e0)

~

Y1+T+i~

(2)

,

P,~EP~(E~, E 1n Ti(~n) 0÷1,J,~,J~+1)= JnfJn+i+sn

(3) D

2J~÷

0

~Dn(En,

j~)= ~xf 0

cIEn+i ~

1n+i 1~n~ (4)

where I and i are the spins of the target and projectile. E~indicate the energy and ~n the spin of the levels of the nth compound nucleus. En, 1,~and s,~indicate energy (in C.M. system), angular momentum and intrinsic spin of the nth emitted particle, and Q’s are mass-differences. The sums over angular momenta are limited by the triangular rule. The sum over x in (4) is extended to all types of particlesconsidered (a,n,p). T 1(e) are optical model transmission coefficients. The function ~(E, J) is the level density defined, according to the Fermi gas model with equidistant levels, by [10]: ~~2(E

.r~ =

2

2J+1 12g114 \/(21r) ~ 6h/’4

2 x e’~~~’~’2° ,

e[4a~)1l1’

(E



for E~>Eyrast

(5)

forE
(5’)

with Eyrast = J(J + 1) h2/2J,

Let e 0 be the energy of the entrance channel, E* the energy and J~’the spin of the residual nucleus

where J was assumed the rigid inertia given by ~mr0A 5/3~

rotor momentum of

C. Savelli and M. Morando

The parameters involved are: a proportional to the single particle level density [10] g, i~ the energy shift to take into account the even or odd nature of the nucleus. It is equal to ko, where ~ is a constant and k is 0,1,2 for even—even, odd-A and odd—odd nuclei, respectively, a the spin cut-off. It may be constant or proportional to the square root of the nuclear temperature t, depending on the input data. This is defined by: at2 t = E It is reasonable to add the following definition: &1(E, J) ~(0.5,J), for 0 ~


~.



3. Computational method The integration ove- the energies are performed in (1) and (4) by repeated application of the first order Gauss—Legendre method to 1 MeV steps, that is: Em~

f Emin

spin states

285

gration, the values of the normalization terms D’s in (1) would be calculated at energy steps of 1 MeV. In the code they are calculated for integer values of energy and stored as two-dimensional matrices. This procedure avoids repetitive calculations. Of course it introduces an error, because the integration limits are real numbers and different for each outgoing channel. On the other hand a substantial saving in calculation time is achieved while maintaining a precision of the results comparable to that of the experimental data. The combination of three particles in the outgoing channel gives ten different ways of emission which corresponds to ten matrices, but only three of these are required to stay in memory for each specified emission. For repetitive calculation (same entrance channel) a copy on magnetic tape at the end of the run, may be later utilized thought the parameter ICREA. If an element of D is out of the dimension of the relative matrix, the code gives a diagnostic and the calculation stops. 4. Code specification The code consists of a main part and five subroutines. These perform the following functions: SUBROUTINE LIMIT (KF, J) extracts two parameters from the transmission coefficients for incoming and each emitted particle. They are: IEMIN: the threshold energy for emission LMAX(E): the maximum value of angular momentum as function of energy.

E 0+n~E

f(E)dE=

/ Population of high

~ Emin

z~.Ef(Ei÷~) 2 ,

(6)

where i~.E= 1 MeV and n is such as: IEmax En I 0.5 MeV. The sums over the angular momentum in (3) are performed according to the conservation law, that is: ~ ~ 5i Imax 4.i T z+1 11(e~)= s T11(e~) (7) —

_~

I ,+i —sRI IJiSI 1imax is the minimum between where maximum allowed 1-value [limax(~i)]

If, + SI and the in (I) at the considered energy of outgoing particle, given by: T 11(e~)~ 0.01. As consequence of the adopted method of inte-

SUBROUTINE DENO (SUM, IE, IJ, H, KK, N, El, NOSI) calculates the denominators D,(E~,.J7) according to (4). SUBROUTINE TRA (BJI, BJF, K IEP) performs the sums of transmission coefficients according to (7). FUNCTION OMEGA (EM, AJM, KD, EYR) calculates the level density according to (5). The spin cut-off parameter is taken as constant, equal to SCUT (input parameter), or proportional to the nuclear temperature in the form (SCUT-t)1/2 respectively for KOV1 = 0 or 1. (see table 1). SUBROUTINE CREA (ICREA, Nl ,N2,N3) formats the magnetic tape, reads old matrices from the same.

C. Savelli and M. Morando /Population of high spin

286

ICREA = 0 formats the magnetic tape for the new matrices, named Nl,N2,N3. ICREA = 1 reads old matrices from the tape. ICREA = 2 as ICREA = l,but resets matrix NI.

5. CDC FORTRAN statements \

1..

-~

a) ~ use Os uie statement LEVEL N, A1, An ...,

was necessary because the code exceeds the dimension of the small core memory of our computer configuration. The meaning of the parameters are: A1, A,~are variables or arrays previously declared in COMMON, DIMENSION or DATA statements. These data are: N = 1 small core memory resident = 2 large core memory resident (directly adressable) = 3 as 2, but accessed by block transfer to or from small core memory. b) The movement of data from disk to large core memory is executed by the following subroutines: OPENMS (LU,IF,LIF,IP) READMS (LU,IFWA,N,I) WRITMS (LU,IFWA,N,I) Where the parameters have the following meaning: LU = logical unit number IF = first word adress of the index LIF = length of the index IP = 1 indicates a name index 0 indicates a number index IFWA = large core memory adress of the first word of the record N = number of the large core memory words to be transferred I = record number. ...,

6. Input data specification The list of input parameters is given in table 1. The meaning of most of the parameters is given in the output sample. Table 1 consists of three parts: the first contains the parameters of the entrance channel or common part of the output channels, the second

states

Table 1

Input

data

Format 7A1Ø

TMAS, PMAS, FMASØ, TJ, PJ, QO (((Q(KK,K,N), KK = 1,6), K = 1,3), N = 1,3) (((KD(KK,K,N), KK = 1,6), K = 1,3), N = 1,3 LE!, LEF, JUMP ((T(K,L,4), L = 1,40), K = 1, KF4) CONTR(= 1.11)

F7.3 F7.3 13 13 18F4.2

((T(K,L,l), L = 1,40), K = 1, KF1) CONTR(= 2.22) ((T(K,L,2), L = 1,20), K = 1, KF2)

18F4.2

CONTR(= 3.33) ((T(K,L,3), L = 1,20), K = 1, KF3) CONTR(4.44) A.Kos, DELTA, RO, C0V1, SCUT W CNUC RNUC Ll,L2,Ll2 (Li ~ LEI, L2 ~ LEF) Kl K2 K3 FMAS2, FMAS3, FMAS4 (EF(M), M = 1, 10) (AJF(M), M = 1,10) ICREA IANCO

18F4.2 l8F4.2 F7.3 7A1Ø A4 A4 13 Al F7.3 F7.3 F7.3 13 13

________________________________________________ parameters of the level density function and the third parameters determining the selected output channel. For each run of the code, the transmission coefficients are read in the following sequence: the T(K,L,J) relative to the heavy-ions (J = 4), two cards for each energy (forty data) repeated from the energy value LEI to LEF at step of JUMP; after these, the transmission coefficient for alpha (J = 1, forty data per energy), for neutron (J = 2, twenty data per energy) and for proton (J = 3, twenty data per energy). The coefficients for light particles must be given at energy steps of 1 MeV from 0 MeV to at least the maximum required energy for the reaction under study. The code calculates the maximum allowed energy for the outgoing particles, reads the needed value of the transmission coefficient and skips the remainder cards to the control card (CONTR). The third part of table 1 begins with a comment card about the studying reaction (W). The successive cards contain the compound (CNUC) and the residual (RNUC) nucleus.

C. Savelli and M. Morando / Population of high spin states

The meaning of ICREA is given in the description of the subroutine CREA. IANCO, the last parameter, stops the calculations if it is set equal to zero, otherwise the code read a new set of data beginning with the comment card W and the calculation goes on. During the calculations the code gives four types of diagnostic after which the job is aborted. The first type is written when the data contains too few transmission coefficients: ERROR ‘part.type’ FEW TRANSMISSION COEFF. The second indicates that the dimension of the matrices D’s is too small (see section 3): nth DIMENSION of Dn TOO SMALL. —

The third is: ENERGY IS TOO SMALL FOR EMISSION OF n PARTICLES. The last one indicates that the probability to populate a level is close to zero. It corresponds to a zero value of an element of the D’s: LEVEL N. m,D~(n1,n2) = 0.

RIGHO nuclear radius. E4, CJ4 energy and spin of the considered level in residual nucleus. —



8. Test case The reaction 44Ca(7Li, 2n)49V was taken as a test. For this calculation the parameters are taken as follows. The transmission coefficients for heavy ions were calculated with the ABACUS Code, using optical potential parameters taken from the elastic scattering of 7Li on 44Ca data [11]. The level density was defined by the following parameters [seeeq. (5): r 0 = 1.44 fm,a 6.5 MeV~,a= 3 and~= 1.5 MeV. For neutrons [12], protons [13] and alphas [14] the existing tabulation of transmission coefficients were used.

References 11] P. Thieberger, A.W. Sunyar, P.C. Rogers, N. Lark, O.C. Kistner, E. der Mateosian, S. Cochavi and E.H. Auerback, Phys. Rev. Lett. 28 (1972) 972; E. Nolte, Y. Shida, W.

7. Common vanables SPIN (4) spin of involved particles. STRA transmission coefficient sum. T(60,40,4) transmission coefficient array. LMAX(60,4) maximum angular momentum for every energy and particle IEMIN (4) threshold energy for emission of partides. Q(6,3,3) Q-values. KD(6,3,3) parameter of level density formula related to the residual nucleus: k in = k& (see (5)). Dl (7,40) D2( 120,40) D3(90,40) Normalization factor for the 10 (Dl), 2°(D2)and —















287





3°(D3’lsten NOXI(40) Master index of random access file. NE1, NJ1, NEJI NE2, NJ2, NEJ2 dimensions and length of the matriNE3, NJ3, NEJ3 ces Dl, D2 and D3, respectively. OKOST, AKOS, GKOS, DELTA, SCUT, KOV1 parameters for level density formula (5). —



Kutschera, R. Prestele and H. Morinaga, Z. Phys. 268 (1974) 267.

[21 W. Hauser and H. Feshbach, Phys. Rev. 87 (1952) 366. [3] F.H. Ruddy, B.D. Pate and E.W. Vogt, Nuci. Phys. 127A (1969) 323. [41 M. Blann, Phys. Rev. 157 (1967) 860. [5] R.L. Robinson, H.J. Kim and J.L.C. Ford, Jr., Phys. Rev. C9 (1974) 1402. [6] M. Uhl, Acta Phys. Austriaca 31(1970) 245. [7] C. Savelli, M. Morando and C. Signorini, Lett Nuovo Cimento 15(1976) 33. [8] A.M. Stefanmi, Padova University, Private Communica-

19] T. Ericson; Advan. Phys. 9 (1960) 425; M. Bohning, Proc. Intern. Conf. on Nuclear reactions induced by heavy ions (eds. R. Bock and W.R. Hering; NorthHolland, Amsterdam, 1970). [101 U. Facchjnj and E. Saetta Menichella, Energia Nucl. 15

(1968) 54. [11] K. Bethge, C.M. Fou and R.W. ZurmUhle, Nuci. Phys. A123 (1969) 521. [12] A. Lindnner, JkF 17 (1966). [131 G.S.Mani,M.A.Melkanoff and F. Ion, Report CEA, 1141 J.R. Huizinga and G.I. Igo, Report ANL, 6373 (1961).

C. Savelli and M. Morando / Population of high spin states

288

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C. Savelli and M. Morando / Population of high spin states

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C. Savelli and M. Morando / Population of high spin states

290

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