Absolute cross sections of compound nucleus reactions

Comp Comr

Computer Physics Communications 77(1993) 396—402 North-Holland

Absolute cross sections of compound nucleus reactions O.A. Capurro TANDAR, Departamenlo de FIsica, Comisión Nacional de EnergIa Atómica, Al’. del Libertador 8250, 1429 Buenos Aires, Argentina Received 2 June 1993

The program SEEF is a Fortran IV computer code for the extraction of absolute cross sections of cc reactions. When the evaporation residue is fed by its parents, only cumulative cross sections will be obtai] gamma ray measurements. But, if one has the parent excitation function (experimental or calculated), this possible to determine absolute cross sections of any exit channel.

PROGRAM SUMMARY Title of program: SEEF

Memory required to execute wit/I typical data:

Catalogue number: ACPJ

No. of bits in a word: 32

Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this issue)

Peripherals used: terminal, line printer of 132 Keywords: gamma-rays, activity measureme sections, nuclear reactions, excitation functic

Licensing protisions: none Computer for which the program is designed and others on which it has been tested: Computers: VAX 11/780, IBM 370; Installations: Departamento de Fisica, CNEA, Buenos Aires Operating systems under which the program has been tested: VMS V4.5

Nature of physical problem One of the experimental methods used to sections of compound nucleus reactions is I ray measurements. These rays are emitted di. tive decay of evaporation residues. Nevert] compound nucleus evaporates charged parti evaporation residue is fed by his parents irradiation. So, one cannot talk of absolute these cases.

Programming language used: Fortran IV _________

Correspondence to: O.A. Capurro, TANDAR, Departamento de FIsica, Comisión Nacional de EnergIa Atdmica, Av. del I ihprt,~rIr~r R~5fl 14~IQ

~

~

Ar~,~ti~

Method of solution This code permits to obtain absolute cro determined isotope. To do this, one needs functions associated with it.

O.A. Capurro

/

Absolute cross sections of compound nucleus reactions

LONG WRITE-UP 1. Introduction

One of the typical processes that occur in the collision between two nuclei is their fusion. This unique nucleus (named the compound nucleus, CN) is in an excited state for a short time; then, it decays by emission of some particles (usually neutrons, protons and alpha particles). This evaporation continues until the excitation energy of the residual nucleus is lower than the threshold energy for emitting any particle. Afterwards, the residual nucleus (named evaporation residue, ER) goes on deexciting by emission of gamma rays to reach the ground state. Generally, the ER will not be a stable nucleus. So, it will disintegrate through subsequent radioactive achieve nuclear stability line. This decays is the to reason whythe some channels are fed by predecessor members of the radioactive chain. It happens during and after irradiation. So, the final activity at the off-line measurement time will not only correspond to the channel of interest but will have extra contributions coming from its parents. It is of interest to obtain excitation functions in experiments for studying nuclear reactions of a compound nucleus. So, it is necessary to determine the absolute activities in each exit channel. Then, if one supplies the parent excitation functions, the code SEEF allows the extraction of absolute cross sections by discounting cumulative spurious activities in channels of interest, 2. Theory The nth member activity of any chain has a recurrent expression that can be seen in some text books [1].Then, the nth member activity at time t after irradiation time T is given by

where p1,1+1 is the branching ratio fr to element I + 1, A1 is the decay co element i, T is the irradiation tin atom number of the target, 4) is the is the absolute cross sections for the the element k. The last term of th corresponds to the produced activil in the evaporation residue of intere terms (k = 1, n 1) conform th activity through disintegrations of members in the chain. I will nam “reaction activity” (RA) and the activity” (DA). The idea is to discount the spu DA in the measured activity A~(t).1 extract absolute cross sections of0’kt] ber, To do this, knowledge of 1) o’,,. is necessary. Now, let us consider the case in are more than one ways of accessin~ in question. This situation is preser of the radioactive nuclei have two meric states. For major clearness, I i the term of interest in compact not~ . ..

,

—

DA~(t)=

n—i

~

~~~11+1~

{Nffk4)(’i~P/l+l)

XE[~UAA jk

,k —

A1

1

where ~ = N4) is constant for eacF summation. It will be wrong to calc for each chain that leads to the nth and then do their summation. Other be summing the same term twice o in some occasions. Therefore, the I have to contain all terms starting v k th element and ending with the ni different ways: n—i

DA~(t)=

~

1’t~

where the function —

exp(—A1T))

(1~~

A 1, T,

1.

k~1

A~(t)= k= ~1

—

s ~

\j=1 Fjk(P1,+l, A1,

T

for the jth chain originating from ment. Up to now, I have supposed a t”~ c t1..,~ ~

inf~ncf~, ~

398

O.A. Capurro

/

Absolute cross sections of compound nucleus reactions

I will consider it explicitly now. Firstly, let us divide the irradiation time, T, in m equal intervals. The T’ time of each interval will have to be short enough to ensure a constant flux in it. Then, the spurious activity in each interval i will be DA1~(t)

n— 1 ~j

~

/

s

~

)

A,, T’, t

~k(Pl,1+l,

1’) k

1

,

\ 1= I

where i~, N4)1, T’ T/m and ti’ t + T iT/rn. The summation of these terms from i 1 to I m will give the total “decay activity” of the nth element. On the other hand, the “reaction activity” after m irradiation intervals will be =

=

The input file for the code is rea and the output file is written to uflil The calculation of the DA~ act the following information: (i) Characteristics of the ER and ol

(4) =

3. Program structure

—

=

tive decay: This includes the ER channel to 1 and a description of all the nuclei the different radioactive chains (h~ sections of the parents, branchin specification of the various radioact

=

RA~(t) o’~(1 exp( —A~T/m)) =

—

x exp( —A~T/m)~

~,

exp(iA0T/m).

I

(5)

(ii) Irradiation characteristics: One must provide the total time and the charge of the projectile. A to the selected option for the data beam, it will have to give the irrac and the beam flux (option a), the c charge (option b) or the collected c interval of irradiation (option c).

Finally, one can obtain absolute cross sections from this last expression. When an element formed by more than one isotope is irradiated, the same product is ohtamed through different nuclear reactions of each isotope. Therefore, the total production of a certam nuclide (o~~) is given by the contributions corresponding to different nuclear reactions (o~):

(iii) Characteristics of the target: Superficial density and atomic weig] (iv) Characteristics of the measuren This includes the number of detecte in the counting interval, the dead the end of irradiation and the beg measurement, the time of the cou and the efficiency and the absolut

cr1= ~Jo~= ~B~A0~W,/a,,

the gamma ray.

i

(6)

I

where B~is a constant for each of the nuclear reactions that give the same product P and A~,is the activity of the isotope of atomic weight W’ and isotopic abundance a1 at the end of irradiation. Then, one can define “cumulative cross sections” as o’c= Eo,a1/Wc=B~A1,

(7)

£

4. Description of the input Free format is used unless other~ In the notation used in this des supposed that if an array depends one variable, they must be given ft to the outermost variable. All the lated to time must be given in minu Input line number 1:

where A1 is the total activity of product P at the 0~k end In these cases, the (k of 1, irradiation. n) are cumulative, the when nth element

Read(80A1), TITU Input line number 2:

crncc ce~tinnwill alsn he ciimii1~tive

Rp~iI1(*’l IMAX

=

. . .,

IMAX

NI. PA

O.A. Capurro

/

Absolute cross sections of compound nucleus reactions

IMAX: number of the different radioactive chains associated with the ER of interest. LMAX: total number of component nuclei in the chains. NL: number of energies. PA: atomic weight of irradiated isotope (in grams). PLT: a graph of cross section versus energy will only be done if this number is not zero.

Input set number 7: It contains 2 * IMAX cards. Read(80A1), (TITL(m),m = 1 to Krv TITL(m): here one can introduce cc

Input line number 3: Read(*), TIRRA, TINT, ZP, QTOT, PHI, EPHI, SU, ESU TIRRA: total time of irradiation. TINT: irradiation time for each interval in which TIRRA is divided. ZP: charge of projectile. QTOT: collected total charge during the irradiation (for option b). PHI: irradiation flux (in particles/(s cm2)) (for option a). EPHI: error of irradiation flux (in particles/(s cm2)) (for option a). SU: irradiated surface of target (in cm2) (for option a). ESU: error of irradiated surface of target (in cm2) (for option a).

cates presence of nuclide and “0” ii

Input set number 4: Read(*), (T12(i),i = ito LMAX) T12(i): half life of each nuclide. Input set number 5: Read(*), (QINT(j),j = 1 to NMAX) QINT(j): collected charge during the j-th interval of irradiation. NMAX (= TIRRA/TINT): number of equal bins in which TIRRA is divided (for option c). Input set number 6: Read(*), (SIG(i,l),ESIG(i,l),i = 1 to (LMA.X-1),l = 1 to NL) SIG(i,l): values of the cross sections for the formation of each parent nuclide (in millibarns). ESIG(i,l): errors of the cross sections (in mil-

Input set number 8: It contains IMAX cards. Read(*), (NV(k,l),k = ito IMAX,l = NV(k,I): matrix that determines th isotopes of each chain k. The chara

Input set number 9: It contains LMAX cards. Read(*), (PORC(il,i2),il = 1 to LIV LMAX) PORC(il,i2): matrix that determine ing ratio from isotope ii to isotope the elements whose index i2 is great only of interest. So, the remaining take any value. These percents mut to unity. Input set number 10: It contains NL cards. Read(*), (ENER(l), AREA(l), TEM(l), DELTAM(1), 1 = 1 to NL) ENER(l): energy. AREA(l): measured area of photop EAREA(l): error of measured area TEM(l): time between the end of ir the beginning of counting interval. DELTAM(l): duration of counting i Input set number 11: It contains NL cards. *

~

ENER(l): energy. EFF(l): detector efficiency. EEFF(l): error of detector efficienc’ ABGA(l): absolute intensity of gam referred to unity). EABGA(l): error of absolute intent ray (value referred to unity). DENSUP(l): superficial density (in t~r~.TmTc,ut\.

-,-..:

~

..1...~:

400

O.A. Capurro

/

Absolute cross sections of compound nucleus reactions

95Zr(0.9%) Y5mNb(9750/ Chain Chain 3: 4: 95Zr(99.1%) Chain 5: 9SmNb(975%) 95~Nb —~

________ I

—~

\icc::

—~

In this case, the matrix NV(k,I) is: Chain 1: 1111

________

o.g ~g.i

Chain 2: 11 0 1

::\\

Chain 3: 0 111 Chain 4: 0 10 1 Chain 5:0011

8~

Q757

and the matrix PORC(il,i2): ~

~Nb Fig. I. Decay scheme of 95Y used in the test run.

Input line number 12: Read(4A1), GUI, AST, BLA, PAR. It suggests using the symbols respectively, “—“,

“~

“~“,

“

“

and

“,

5. Test run To illustrate the use of this program I have constructed a hypothetical example based on the decay scheme shown in fig. 1. For every step of the decay the figure shows the half-life of the nuclide and the probability of each decay mode. The ER of interest is ~Nb coming from an enriched target of 94Zr through a (a,p2n) reaction. Nevertheless, this isotope is fed during and after irradiation by other ER’s: 95Y ((a,3p) reaclion), 95Zr ((a,2pn) reaction) and 95mNb ((a,p2n) reaction). So the total number of nuclides is four (LMAX = 4) in this example. From the decay scheme, it can be seen that ~Nb is associated with five decay chains (IMAX = 5). They are: Chain 1: 95Y(100%) 95Zr(0.9%) 95m Nb (97.5%) 95~Nb Chain 2: 95Y(100%) 95Zr(99.1%) 9~Nb —

-~

—~

—*

—*

0. 1. 0. 0. 0. 0.009 0. 0. 0. 0.0.0.

0. 0.991 0.975 0.

The total irradiation time, which to be 100 minutes (TIRRA) was equal intervals of 1 minute (TINT = TIRRA/TINT = 100). The intensit~ be variable but constant in each int~ For demonstration purposes, 10 sim mental points were included in the As it has been established, it is have the absolute cross sections 01 perimental or calculated) that feed i interest. So, the excitation function: and 95mNb are simulated. Besides, t (AREA(I)), the dead time (TEM(l)) of the counting interval of each (DELTAM(1)) and the superficial target (DENSUP(l)) are fictitious. In addition to net areas and crc graph of the excitation function ca as output.

Reference [i] E. Segrc, Nuclei and Particles, 2nd Cummings, London, 1977).

OA

Capurro

/

Absolute cross sections of compoundnucleus reactions

TEST RUN Input file (unit 4) CROSS SECTIONS OF 942R(ALFHA.P2N)953N9 REACTION 4 10 93.9063 0 100.0 1. 2. 0.0 0. 0. C. C. 10.3 92160.0 5220.0 50400.0 0.6269E+16 0.6269E+16 0.6269E+16 (l.32~9E+16 0.6269E+1b 0.6269E+16 0.6269E+16 0.6269E+16 0.6269E+16 0.62~9E+1b 0.5985E+16 0.5985E+16 0.5985E+16 0.5985E+16 0.5985E+16 0.5985E+16 O.5985E÷16 0.5985E+16 U.5985E+16 0.5985E+i~ 0.3150E+16 0.3150E+16 0.3150E+16 0.3iSOE±1o 0.3150E+16 0.3150E+16 0.3150E+16 O.3150E+16 0.3150E+16 0.3150E+lc 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 O.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E÷16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+16 0.6300E+1~ 0. 0000E+00 0. 0000E+00 0. 0000E+O0 0. 0000E+00 0. 0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E÷00 0.0000E+00 0.0000E+0O 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.3150E+16 0.3150E+16 0.3150E+16 0.3150E+16 0.3150E+lb 0.3150E+16 0.3150E+16 0.3150E+16 0.3150E+16 0.3150E+1~ 0.3150E+15 0.3150E+15 0.3150E+15 0.3150E+15 0.3150E+15 0.3150E+15 0.3150E+15 0.3150Ei-15 0.3150E+15 0.3150E+15 0.3150E+14 0.3150E+14 0.3150E+14 0.3150E+14 0.3150E÷14 0.3150E+14 0.3150E+14 0.3150E+14 0.3150E+14 0.3150E+14 5

6.00E+00 2.IOE+00 3.20E—01 0.OOE+00

5.OOE—01 2.20E—01 4.00E—02 0.OOE+00

4.50E+00 5.OOE—01 1.32E+0O 1.6OE—01 5.OOE—02 7.OOE—03

3.20E+O’O 3.SOE—01 7.SOE—0l S.OOE—02 0.OOE+00 0.OOE+00

2.OOE+0i 1.84E+0i 3.80E+00 0.00E+00

2.60E+00 1.OOE+00 5.OOE—0l 0.OOE+00

2.1OE+01 2.15E+O0 1.40E+01 1.90E+00 9.60E—0i l.IOE—01

2.15E+0i 2.20E+00 8.60E÷O0 7.90E—01 1.OOE—01 1.SOE—02

3.SOE+01 4.SOE+01 1.70E+0l 5.OOE—02

3.OOE+00 3.00E+00 2.OOE+00 l.OOE—02

4.20E+01 3.50E+0O 4.OOE+01 3.OOE+00 6.75E+00 9.OOE—01

4.50Ei-01 .60E+00 3.OOE+01 3.50E+00 1.23E+00 2.50E—0l

VIA 1

95fl100.%.

9SZR(0.9%.

VIA 2

95Y(100.%)

9SZR(99.1%)

95MNE:i97.5);.

95CN8 95CN8

VIA 3

95ZRC0.9~.)____95r’1NB97.5i~____950N8

VIA 4

95ZR(99.1)~)

95GNE~

VIA 5

0. 0. 3.

1 1 0 0 0

9SMNB 97 .~__956NS 1 1 1 1 0

1. 0. 0. 0. 121.1 109.7 100.5 91.2 79.4 69.9

59.o

50.3 38.8 30.0

121.1 109.7 100 5 91 .2 79.4 68.9 59.6 50.3 38.8

1 0 1 0 1

1 1 1 1 1

0. 0.039 0. ~i,

280000. 300000. 323000. 310000. 230000. 240000.

150003. 43000. 15000. 3~00. 0.03 0.06 C b 0.33 0.09 0.09 0.08 0.08 0.09

0. 0.991 0.975 0. 14500. 14600. 14700. 14800. 14900. 15000. 11000. 43,33. 1500. 700.

0.304 0.004

4 0.004 0.004 0.004 0.004 0.004 0.004 L

10.

800 310 620 930 340 850 8~0

10. 10. 10.

10. 10, 10. 10. 10. 10.

630 390 3.0998 0.0998

fl999

0.0993 0.0993 0.0998 0.0993 0.0998 0.0998

0.301 0.OOi r 00~ 0.001 0.001 3.001 0.001 0.001 0.001

.0i~45 .01445 ~~45 .01445 .01445 .01445 .01445 .01445 .01445

.30144 .00144

cC ~‘, .00144 .00i~ .00144 .00144 .00144 .00144

402

O.A. Capurro

/

Absolute cross sections of compound nucleus reactions

Output file (unit 6) CROSS

SECTIONS

Number cf chains Tct.~1 number Number cf

:

OF

94ZRIALPHA.P2N)950N0

REACTION

5

cf ccmpcnent

ener~ier

nuc leide

4

10

CROSS SECTIONS 09 EACH FARENT NUCLIDE 6.UOE+00 2.1OE+00 3.20E—01 0.OOE+00

+— +++-

2.OOE+01 1.84E+01 3.80E+00 0.OOE÷OC: 3.SOEi-01 4.50E+C1 1.70E~01 5.OOE—02

+—

÷— +— +—

+— +— +— +—

4.50E+00 1.32E4-00 5.00E—02

+—

2.6OE+00 2.OOE+OC: 5.OOE—01 0.~0E+00

2.1OE+01 1.40E+01 ..60E—01

4-—

3.COE+00

4.2OEi-01 4.OOE+01 o.75E+00

5.OOE—01

2.20E—01 4.COE—02 0.00E+00

3.OOE+00 2.00E+00 1.OOE—02

VIA 1

95V110C.YJ

95ZR10.9V.)

VIA 2

95Y1100.5

952R199.11

+—

+—

+—

+—

‘— +— +—

5.OOE—01 1.60E—01 7.00E—03

3.20E+00 +— 3.ZOE—01 7.SOE—01 +- E.COE—C2 0.OOE+00 +— C .0OEi-OC

2.1SE+00 1.90E+00 1.1OE—01

2.15E+01 8.óOEiOO l.OOE—01

3.SOE+00 3.005+00 9.OOE—01

4.SOE+01 3.OOE+01 1.23E+00

95MN0157.5;1;

+—

2.20E+oC

*-- 7.9C:E—31 +—

1.90E—3

~— +—

3,50E+03

+—

~.50E—01

950N0 956N3

VIA 3 :

95Z~(0.9~) _~

VIA 4

952F:199.1’/.)

VIA S

95MNt~97.5)1) __95GN3 956N0 9SMNE97.5).)_9SGNE.

E(MEV>

TOTAL AREA

111.1 109 7 100 5 91.2 79 4 68 9 59.6 50.3 38.2 30 c’

0.280E+Oa 0 3OCE+Ob 0 3205+06 0.310E+06 0 ~30E+~e 0 ~40E+~e 0.150E+0& 0.480E+0S C.1SOE+0S 36UE+L4

NET AREA 0.213E+0~ u _E+0~ 0 ~0E+0~ 0.229E+06 r ~0~E+0~ C 185E+06 0.119E+0~ 0.3565+05 C.127E÷05 u 3EiE+0~

+— +— +— +— +— +— +— +— +— +—

0.155E+05 0 259E+LE

u 1~1E+u5 0.162E+O5 0 1eIE+05 0 1SSE+0E 0.113E+05 0.493E+04 0.152E+04 0 r~ E~ 3

CROSSECTION IMOARN) 0.1345E+02 i~ 3.3129Er0i ~ 14_~E+0 i~— ~ 3.~ E’. 1514E+u ~— ~43 E’~ 0.1448E4-02 +- C.333aE+0 i. 1313E~0. ~— C 3~1uE’0 1 72E.-L ~— r~ ~6~E+ 0.751oE~0i +— 0.1917E~0: 0.2251E~01 ÷— C.671C:E÷Cc 0.8047E±C0 *— 0 244E+OC ~3E+ ~— r