Cross sections of the (n,p) reaction on zirconium isotopes

Nuclear Physics North-Holland

A510 (1990) 93-105

CROSS

SECTIONS

OF THE (n,p) REACTION

ZIRCONIUM A. MARCINKOWSKI,

U. GARUSKA’,

H.M.

ON

ISOTOPES* HOANG,

D. KIELAN

and

B. ZWIEGLINSKI

Soltan Institute for Nuclear Studies, 00-681 Warsaw, Poland Received 29 May 1989 (Revised 25 September 1989) Abstract: Cross sections for the (n, p) reaction on 90.9’*92,94Zr targets have been measured in the neutron energy range from 13 to 16.6 MeV and have been compared with predictions of the statistical and DWBA theories of multistep processes.

E

NUCLEAR

REACTIONS

90,9’,92.94Zr (n, p), E = 13-16.6 MeV; measured and DWBA multistep theory analysis.

o(E).

Statistical

1. Introduction The measurements of cross sections for the neutron induced threshold reactions as a function of the incident neutron energy are, besides of interest from the viewpoint of validation of nuclear reaction models, of primary interest for practical applications. This is particularly true for reactions on isotopes of zirconium, since Zr is a constituent of structural materials for fission reactors and a potential material for construction of future fusion reactors. So far the excitation curve for the (n, p) reaction has been measured on the lightest isotope 90Zr only ‘). Measurements for the heavier zirconium isotopes are scanty and confined to neutron energies around 14 MeV. These facts and the initiatives within the IAEA coordinated project on “measurements and analysis of fast neutron nuclear data” stimulated us to measure cross

sections

of the (n, p) reaction

on isotopes

of zirconium

in an activation

experiment with projectile neutrons of energies in the range from 13 to 16.6 MeV. The present paper summarizes experiments performed with the 3 MeV Van de Graff accelerator of the Institute for Nuclear Studies in Warsaw. The experimental procedure and the corrections that convert the measured activities of the irradiated samples into absolute integral reaction cross sections are described in sect. 2. In our earlier analyses of the (n, p) reaction cross sections, on several isotopic chains in the medium-mass domain 2), we used the geometry-dependent hybrid model 3, for calculating the preequilibrium emission cross sections. This model * Work supported by the IAEA Contract ’ Permanent address: University of todi, 0375-9474/89/$03.50 (North-Holland)

0

Elsevier

Science

No. 4836/Rl/CF. todi, Poland.

Publishers

B.V.

A. Marcinkowski et al. / Cross sections

94

accounts

for the enhanced

reaction

proceeds

projectile

impact

tory agreement

emission

in spherical parameter.

between

tion of the isotopic

from the nuclear

shell-shaped These analyses

theory and experiment

dependence

surface

by assuming

regions

of a radius

indicate

that, although

can be obtained,

of the measured

cross sections

that the

determined

by the

overall

satisfac-

the detailed

descrip-

required

parameter

adjustment. In the present paper the more rigorous treatment of preequilibrium emission, such as the statistical multistep compound and the multistep direct processes, in the framework of the quantum-mechanical theories developed by Feshbach et al. “) (FKK) and Tamura et al. 5), was applied in the calculations. The theoretical formalism is formulated in sect. 3. The results of calculations are compared with the measured cross sections of the (n, p) reactions on 90Zr, 9’Zr, 92Zr and 94Zr targets in sect. 4. Our summary

and conclusions

2. Experimental

are given in sect. 5.

procedure and results

The monoenergetic neutrons were obtained by bombarding tritium absorbed in a thin layer of titanium (500 pg/cm*) deposited on a copper backing with deuterons accelerated up to 1 MeV. This energy determined the outgoing neutron energy range. The deuteron current was about 40 PA. At higher deuteron energies the output of the t(d, n)4He source reaction was too low for inducing measurable activities in the irradiated zirconium samples. The energy of neutrons was selected by the choice of the emission angle. The neutron energy spread was evaluated from the effective energy distributions of neutrons incident on the samples, which were calculated by the Monte Carlo method. This calculation accounted for the irradiation geometry, the deuteron energy loss in the tritiated titanium layer, the dependence of neutron energy upon the emission angle and the angular distribution of the emitted neutrons. The fluctuations

of the neutron

flux during

irradiation

were monitored

by counting

protons recoiling from a thin polyethylene foil, with the use of a Cs(TI) scintillation crystal in a multiscaler mode. The samples of natural zirconium were spectroscopically pure metallic cylinders, manufactured

by Johnson

Matthey

& Co, which were placed

2.5 cm from the beam

spot on the tritium target. They subtended the solid angle of about 0.08 sr. The absolute neutron flux was determined by irradiating iron samples in the same geometry but in a separate accelerator run and by referring to the well-known cross sections of the 56Fe(n, p)56Mn reaction “). The reaction products were identified by measuring their characteristic y-rays and half-lives with a 80 cm3 Ge(Li) spectrometer, equipped with standard ORTEC electronics and a ND-4420 analysing system, which allowed programming and automatic timing of the measurements. The decay of the neutron induced y-activities was measured usually for more than three half-lives and extrapolated to the end of irradiation by using a FORTRAN subroutine. Only the relative efficiency needs to be known for detecting y-rays in the Ge(Li) crystal when referring the investigated

A. Marcinkowski

activities energy,

to the activity

of the iron standard.

was determined

with well-recognized Irradiation different

of natural

reaction

This efficiency,

with use of standard

intensities

radioactive

of outgoing

samples

product

which

as a function sources

of y-ray

‘69Yb and 226Ra

y-rays ‘).

has the advantage

nuclei,

95

et al. I Cross sections

that it produces

can be easily

separated

simultaneously because

of the

excellent energy resolution of the Ge(Li) detector. On the other hand, this method has a drawback because it requires a more sophisticated data-reduction procedure, when reactions on different target isotopes lead to the same product nucleus. In such cases a set of differential equations, describing the production and the decay of the nuclei of interest, has to be solved in order to obtain relations between the investigated and the interfering reaction cross sections, e.g. by monitoring the Tl,2 = 49.7 m decay of the metastable product nuclei 91mY one measures grn + 0.59

49.7 m 49.7 m-9.67

h u’

where a,,, is the cross section for the investigated “Zr(n, p)‘lmY reaction and (T is the cross section for the interfering reaction 94Zr(n, a) 91Sr, which is followed by a 9.67 h P-decay of 91Sr to 91mY. Cross sections for the latter reaction have been measured in the present experiment, thus allowing to determine u,. In addition, by measuring the 556 keV y-rays from the 49.7 m decay of 9’mY one determines the cumulative yield of the reactions “Zr(n, p), 92Zr(n, d), 92Zr(n, np) and 92Zr(n, pn). This applies also to the measurement of the 480 keV y-rays from the 3.19 h decay ‘OrnY nuclei. The measured activities have to be corrected for the contributions of the of multiparticle emission, as well as for deuteron emission. These corrections are required at appropriate incident neutron energies and were calculated with the use of the statistical model code EMPIRE “) or taken from experiments, when available ‘). They appeared not to surpass the errors of the cross sections we measured. In table 1 we list all the decay constants

assumed

in the data reduction

TABLE 1 Decay

Reaction

“Zr(n, 9’Zr(n, 92Zr(n, 94Zr(n, “Zr(n, “Zr(n,

P)~‘“Y P)“~Y P)~‘Y P)~~Y a)*‘?r a)“Sr

“) Conversion

data used for reducing

the reaction

E, (kev)

T1/z

480 556 935 919 388 1024

2.19 h 49.1 m 3.54 h 18.7 m 2.80 h 9.48 h

coefficient

yields Intensity of y per decay 0.910 (0.1) “) 0.949 0.139 0.560 0.820 0.330

procedure.

A. Marcinkowski et al. / Cross sections

96

TABLE 2 Experimental

cross sections Neutron

in mb

energies

(MeV)

Reaction

“Zr(n,

p)‘OmY

“Zr(n, P) 9’mY 92Zr(n, P)~*Y

13.4+0.4

13.6*0.3

14.2kO.3

14X*0.3

15.2kO.2

15.4*0.2

15.9*0.5

16.6*0.1

9.8kl.2

11.6ztl.3

11.7k1.4

11.7*1.4

11.9k1.5

11.8*1.4

12.Ok1.7

12.1k2.0

13.1zt1.9

14.8*1.6

16.211.7

17.151.7

17.3zt1.8

16.Ok1.9

18.3i2.9

22.8k3.9

17.6*2.3

20.8k2.6

21.Ok2.6

22.5k3.3

21.9*3.3

14.3*2.6

18.4k2.4

18.3k2.3

94Zr(n, P)~~Y

4.1k1.5

6.0i0.8

5.2*0.X

7.4kO.9

8.3*

‘OZr(n, a) 87mSr

2.6i0.4

3.3iO.4

3.4kO.4

3.7*0.5

4.OkO.6

4.0*0.5

3.350.6

3.6kO.5

94Zr(n, a)“Sr

3.510.8

4.0i0.6

4.1+0.6

4.8*0.7

4.8+0.7

4.6*0.6

5.3+1.1

5.2*

1.0

8.6*

1.0

7.3*

1.6

8.9* 1.9 1.0

The final results were also corrected for summing of pulses in the Ge(Li) crystal due to cascading y-rays and for attentuation of the measured y-rays in the samples. These corrections amounted to 16% and II%, respectively. All cross sections measured in the present experiment are gathered in table 2. Both the statistical and systematic errors are included. The latter consist of: (i) the uncertainty of the reference cross section, estimated at about 3%, (ii) of the error in the integration of the pulse height spectrum, which amounts up to 11% for the weakest radiative transition (see table l), (iii) of the relative efficiency for detection of y-rays, determined with an accuracy of 3%, and (iv) of the y-ray attenuation uncertainty which equals 2%. Another 10% error was added in the quadrature, which is due to the correction

for multiparticle

emission

at neutron

energies

higher than

15.5 MeV.

Recently cross sections for the reactions studied here have been measured in a narrower neutron energy range from 13.3 to 15.3 MeV at JAERI lo). These new results are in excellent agreement with the data presented in table 2. The few single energy

measurements

reported

in the literature

“) display

a considerable

scatter.

3. Theoretical formalism The measured cross sections were analysed in terms of the decay of compound nucleus preceded by the preequilibrium emission. For this purpose an extended version of the computer code EMPIRE was used “). As described in detail in ref. ‘*) the standard, angular-momentum-dependent Hauser-Feshbach theory was applied for the calculation of evaporation spectra and the quantum-mechanical multistep compound emission theory of FKK “) was used to describe that part of preequilibrium emission that appears in symmetric angular distributions. The remaining portion of preequilibrium decay, namely the multistep direct emission, which is characterized by forward peaked angular distributions, can be also calculated in the framework of the quantum-mechanical theory. The theories of multistep direct reactions of FKK “) and of Tamura et al. ‘) derive the one-step cross sections in the same way. The calculational procedures are different however. In the FKK

A. Marcinkowski

theory

the microscopic

DWBA

cross sections

states r3). On the other hand Tamura to get the macroscopic continuum

cross sections.

The latter approach

elementary

comparison

with the angle-

we followed

3.1. MULTISTEP

are averaged

et al. ‘) average

DWBA

and energy-integrated

the procedure

COMPOUND

of Tamura

over many

final lplh form factors

was used in calculating

reduces

cross sections,

91

the microscopic

form factor, which subsequently

the required analysis

et al. I Cross sections

considerably

and is therefore activation

the number

more practical data.

the of for

In the present

et al. ‘).

EMISSION

For the statistical multistep compound emission, due to the decay of a chain of quasibound states of the composite system, the FKK “) theory predicts the cross section

to be, da -= dU

2J+l

TX2

J,rr,:,S,j(21+1)(2i+l)


(1) where i, I, J and S are the spins of the projectile, target nucleus, composite system and the residual nucleus, respectively. The projectile’s total momentum is j’ (j for the ejectile). The term 24T)/(D) is the entrance-channel strength function, which has been related, for the purpose of present calculations, to the optical-model transmission coefficients via a reduction factor R = 0.86. This factor takes into account the loss of flux due to multistep direct processes and was evaluated from the experimental angular distributions “). The depletion factor in the round bracket describes Nth-stage of emission

that part of the flux that survived emission prior to formation of the state in the interaction chain. The last term in eq. (1) is the probability from the quasibound

states of the Nth stage of the reaction.

The latter

emission can occur only via transitions to continuum states in three different ways: v = N * 1, N, called exit modes. The escape width r’ and the damping width r’ are calculated by evaluating the square of the transition matrix element, by averaging over initial states, summing

over final particle-hole states and considering the density orbitals “). The of accessible states, p&, which involve only bound single-particle matrix elements are taken for a S-type residual interaction in order to obtain a factorized

expression

for the widths (r~;yp;y(

U)) = 27r12X”, Y; .

(2)

In eq. (2) I is the overlap integral of the four radial wave functions for the two initial interacting particles/holes and for the two final particles/holes. The functions Y are the densities of levels accessible in the transition and X’s are the angular momentum coupling functions, which contain also the spin-dependent part of the

98

A. Marcinkowski

level density.

The damping

et al. / Cross sections

width factorizes

in a similar

way I*). The total width is

Ntl (IN,)=+

where

summation

Both X and

c v=N-1

over S and j extends

Y depend

(r%“PB

1 Sj

S” (u))

dU,

also over the exit neutrons

on the exit mode

V. In practical

calculations

and protons. one assumes

the exciton representation for the particle-hole states which complexity is determined by the reaction stage N. Then the number of excited particles and holes (excitons) is p + h = n = 2 N + 1. The three possible exit modes Y denote particle-hole creation, annihilation and exciton scattering, respectively. It has been found important to ensure consistency with the definition of the multistep compound process “) and to calculate the Y-functions by assuming only the quasibound residual states instead of all accessible states of the composite system. The densities of states of the former type have been taken from ref. 14). Also the X-functions were evaluated rigorously by considering nucleons as spin-$ particles 12*15).From refs. 127143’6) one finds easily, that e.g. for a transition creating a particle-hole

pair v = n + 2: Y :+2=;gh(h+1)

PpB,ll+1(~) &(E)

xn+2=(2j+1)W+1) nJ

R,(J)

’

C W+ l)R,(Q)(&+ 1)F(j&Ll(j4) Qhh

(5) where j, j, , j,, j,, j4 and Q are the total angular momenta of the ejectile, of the particle and of the hole in the newly created pair, the total angular momentum of the pair, that of the noninteracting core excitons and of the exciton initiating the transition, respectively. The single-particle state density is g and its spin distribution is R,. The function, created pair is

which

describes

angular

WJ = C (2j, + l)Rl(jA2h+

momentum

decomposition

of the

l)R,(jd

hi2

The overlap integral I has been approximated by assuming, that the radial wavefunctions for the active excitons of angular momenta Q, j, j, and j, are constant inside the nucleus. These assumptions result in an analytical formula for I [ref. “)I. The interaction strength V, enters I as a multiplicative factor, which cancels out in the ratios of formula (1). It does not occur either in the entrance channel strength function in eq. (l), which was obtained empirically by evaluating the forward peaked portions of the experimental angular distributions 12) rather than calculated microscopically. Formula (1) contains r - 1 stages, excluding the rth stage corresponding

A. Marcinkowski et al. / Cross sections

to the decay

of compound

were found

to contribute

to calculate

the compound

to the preceding

3.2. ONE-STEP

nucleus.

In the present

significantly. nucleus

For the one-step

calculations

The Hauser-Feshbach

cross sections,

three steps of compound

DIRECT

99

corrected

only three formalism

states

was used

for the loss of flux due

emission.

EMISSION

direct transitions

Tamura

et al. ‘) derived

an expression

of the

form (7) with E, = E, - Q” - Eb, E, and Eb being the projectile and ejectile energies and the Q” value is for the transition to the ground state of M. The model states A4 are lplh states of the shell model. The function CM (E,) is the probability per unit energy that there is state M at an excitation energy E,. In practical calculations one takes, e.g. a lorentzian form for the probability distribution

c,(E,)=(r/~)[(E,-E,)*+r’l-‘,

(8)

with r being the spreading width of the particle-hole strength. Eq. (7) can be further simplified by averaging the microscopic form factors contained in do”/dflb over M. This approach provides for zero spin transfer and even target

d’u(&) dEb

where the spectroscopic

dab

density

=

dury;y eb) , b

F P,(J%)

p,(E,)

(9)

takes the form

dEx) = P: C CM(Ex)(d,M)*

(10)

M

for both inelastic scattering and charge exchange reactions I’). The spectroscopic amplitude d,M is a purely geometric factor. It is taken usually equal unity in order to make sure that all the strength is included in the statistical calculations and /3,‘s are the orbital angular momentum I-dependent parameters, which scale the average form factor.

The total direct

reaction

cross section

for the onestep

transitions

is a

double integral of (9) over the ejectile energy and the emission solid angle. The simplicity of formulae (9) and (10) has been obtained at the expense of introducing the parameters r and /3,, the systematics of which is not yet well established. Theoretical microscopic calculations of pi’s as a function of the excitation energy and transition multipolarity, like those presented by Ignatyuk and Lunev “), have been performed only for a few selected nuclei and may be used only as the first guess of the parameters for zirconium. In practical calculations PI are often assumed independent of 1 [ref. “)I.

A. Marcinkowski et al. / Cross sections

100

4. Calculations The cross sections, incoherent

are compared

sum of the contributions

the multistep contributes,

which

compound in the studied

and comparison with experiment

emission cases,

with experiment,

are calculated

from the decay of the compound and of the onestep

direct

nucleus,

emission.

at most 3% of the total proton

as an from

The latter

emission

yield*.

The two-step direct process was found to be an order of magnitude less important at the projectile energies below 20 MeV [refs. ‘“-“)I and therefore was neglected in the present analysis. The main task of the calculations includes a consistent parametrization of, (i) the optical-model potentials which provide the penetrability coefficients, the distorted waves and the form factors, (ii) the level densities, as well as the particle-hole state densities of the preequilibrium configurations and (iii) the y-ray strength functions. These were chosen in the following way: - Global optical potentials, which were successfully used in Hauser-Feshbach calculations of nonelastic cross sections, were favoured. For neutrons the potential of Moldauer *‘) at energies below 4 MeV and that of Bjiirklund and Fernbach *“) above this energy were used. The potential of ref. 24) was used also for protons and the competitive emission of alpha particles was described with the potential suggested by McFadden and Satchler 25). - The four parameter formulae derived by Cameron and Gilbert 26) were used for calculation of the compound nucleus level densities. The parameters entering these formulae were taken from the extensive systematics of Reffo *‘). The density of the quasi-bound particle-hole states of different exciton complexity, which participate in the multistep compound process was calculated according to ref. 14). The spin distribution of these states was calculated with the spin cut-off parameter, which depends on the number n of excitons u’, =0.28A2’3n [see ref. ‘“)I. - Strength functions for El, E2 and Ml radiative transitions contained single-particle and the giant resonance metrized according to the systematics

the

parts. The giant resonance part was parapresented in ref. *“). Weisskopf estimates

served for the single-particle part “). The calculations of the direct cross sections

were performed

with the neutron-

particle and the proton-hole states of the spherical Nilsson model and the spreading width of r = 4 MeV, taken from Traxler et al. 19). The elementary DWBA angular distributions in eq. (9) were calculated with the code DWUCK-4 30). The distorted waves were calculated with the global optical potentials for neutrons and protons. As far as the radial dependence of the form factor is concerned the microscopic calculation of Tamura et al. ‘) yield a surface peaked shape also for the charge exchange reactions. Therefore we generated the average form factor as a derivative emission contained l This ratio ~~“/(T,,_,, which is usually low, because of the rather large multiparticle in vP,,, differs by definition from the reduction factor R used in the preceding section. The latter equals to the sum of directly emitted neutrons, protons and alpha particles divided by the number of absorbed projectile neutrons, R = (a$ + CT:”+ u$‘)/&“.

A. Marcinkowski

of the real diffuseness

Woods-Saxon

potential

0.65 fm. The deformation

adjusted

to reproduce

reaction,

measured

the angular

by Traxler

for I= O-9, was used throughout

et al. / Cross sections

with the radius parameters distributions

101

parameter

of protons

from

et al. 19) at 14.1 MeV. The resulting our calculations.

1.25 fm and

PI were kept independent

The measured

the

of 1 and

the 93Nb(n, p) value

excitation

/3, = 0.02 curves

are compared with the calculations (solid lines) in figs. l-4. The cross sections for population of the isomeric states (dash-dotted lines) are also shown when measured. The solid lines and the dash-dotted lines represent the sum of three components: the compound nucleus, the multistep compound (msc) and the one-step direct (lsd) cross sections. The compound nucleus cross sections are not indicated but can be obtained by subtracting the sum of the dashed lines (msc+ lsd) from the solid one. The compound nucleus contributes strongly at low energies and for the lightest target isotope 90Zr, in which case the agreement between the theory and experiment is best. With increasing number of neutrons in the target nucleus the evaporation of protons decreases, falling below 10% of the total (n, p) reaction yield for 94Zr. The msc emission rises steeply with the bombarding energy and dominates the reaction cross section at about 18 MeV. The lsd level of l-7 mb in the investigated energy range. brium component of the excitation functions is systematic tendency of the calculated multistep

emission contributes little, at the The description of the preequilisatisfactory, however, there is a cross sections to rise faster with

isd

Fig. 1. Comparison of the calculated cross sections (solid line) for the “Zr(n, p)“Y reaction with experimental data. The triangles are the total reaction cross sections taken from ref. ‘). The circles denote cross sections for population of the isomeric state ““‘Y, measured in the present experiment, squares are from ref. I”). The dash-dotted line is to be compared with the isomeric state cross sections. Both the solid line and the dash-dotted line represent the sum of the compound nucleus cross section, the multistep compound cross section (msc), and the one-step direct cross section (lsd). The total msc and lsd cross sections are separately shown with the dashed lines.

A. Marcinkowski et al. / Cross sections

102

Fig. 2. The same as in fig. 1 but for 9’Zr(n, P)~‘Y reaction.

projectile

energy than implied

by the experimental

The triangles

excitation

are from ref. ‘I).

curves. This behaviour

has been already observed in ref. 2), which applied the hybrid model of precompound emission. It would be desirable to examine whether this trend persists at higher neutron energies. The success of the formalism given above is supported by the analysis of the proton emission spectrum measured by Haight et al. ‘) for the 90Zr+n reaction at 10

ZL

Fig. 3. The same as in fig. 1 but for the 92Zr(n, P)~‘Y reaction. cross sections, as is the theory

J

Both circles and squares (solid line).

are total reaction

A. Marcinkowski

et al. I Cross sections

103

Fig. 4. The same as in fig. 1 but for 94Zr(n, p)“‘Y reaction. Both circles and squares cross sections, as is the theory (solid line).

14.8 MeV. The overall

description

as shown in fig. 5. The applied

10 “o

of the spectral

formalism

I 2

I

Pro&n

distribution

fails in the high-energy

I

are total reaction

of protons

is good,

part of the spectrum,

-‘ik

h-E&

(i&V)

Fig. 5. Comparison of the calculated proton-emission cross sections versus proton energy for reactions data taken from ref. ‘). The horizontal induced by 14.8 MeV neutrons on a “Zr target, with experimental bars represent the experiment. The solid line (to be compared with the experiment) is a sum of the Hauser-Feshbach cross sections for the (n, p) reaction (dash-dotted line cnl), for the multiparticle (n, np) reaction (dash-dotted line cn2), of the multistep compound cross section (msc) and of the onestep direct cross section (lsd).

104

A. Marcinkowski

where the features very low energies. reaction

(cn2) by slight readjustment

nucleus

because

levels are not adequately

In the latter part it is possible

cross section

e.g. the residual pursued

of individual

et al. / Cross sections

level density

the origin

parameter

of deviation

between

accounted

to enhance

for, and at the

the multiparticle

(n, np)

of some of the model parameters, a. However, theory

be caused by inadequacy of the optical transmission very low energies. The (n, pn) reaction contributes compound nucleus calculation.

this way has not been

and experiment

coefficients negligibly

might also

for protons at the according to the

5. Summary The energy

and angle-integrated

cross sections

have been compared

with predic-

tions of the multistep preequilibrium theories. It has been shown that the quantummechanical approach to the multistep processes describes the measured activation cross sections satisfactorily with only one adjustable parameter /3 (I-independent). The applied formalism describes successfully also the proton emission spectra. The predictive power of the quantum-mechanical theory appears not worse than that of the semiclassical preequilibrium models, which have been extensively used in the analyses of the experimental data during the last decade. The measured (n, (Y) reaction cross sections were not interpreted theoretically since the preequilibrium emission of the complex particles has not yet been formulated within the context of the multistep compound theory.

References 1) B.P. Bayhurst and J.R. Prestwood, J. Anorg. Nucl. Chem. 23 (1961) 173 2) A. Marcinkowski, K. Stankiewicz, U. Garuska, and M. Herman, Z. Phys. A323 (1986) 91; H.M. Hoang, U. Garuska, A. Marcinkowski and B. Zwieglinski, Z. Phys. A 334 (1989) 285 3) M. Blann, Nucl. Phys. A213 (1973) 570 4) H. Feshbach, A. Kerman and S. Koonin, Ann. of Phys. 125 (1980) 429 5) T. Tamura, T. Udagawa and H. Lenske, Phys. Rev. C26 (1982) 379 6) D.E. Cullen, N. Kocherov and P.M. McLaughlin, IAEA Report IRDF-82, IAEA-NDS4l/R (1982) 7) P. Alexander and F. Boehm, Nucl. Phys. 46 (1963) 108; R. Gunnik, J.B. Niday and R.A. Mayer, Report UCID-1539 (1969) 8) M. Herman, A. Marcinkowski and K. Stankiewicz, Comp. Phys. Comm. 33 (1984) 373; A. Marcinkowski, Lecture on EMPIRE code, presented at Workshop on applied nuclear theory and nuclear model calculations for nuclear technology applications, March 1988, Trieste ICTP, ed. M.K. Mehta, J.J. Schmidt (World Scientific, Singapore, 1989) p. 726 9) R.C. Haight, S.M. Grimes, R.G. Johnson and H.H. Barshall, Phys. Rev. C23 (1981) 700; S.M. Qaim, Nucl. Phys. A382 (1982) 255; Activation cross section measurements, Report JAERI-1312, March 1988 10) Y. Ikeda, C. Konno, K. Oishi, T. Nakamura, H. Miyade, K. Kawade, H. Yamamoto and T. Katoh, in Progress report of JAERI, Sept. 1986, ed. Report INDC (JPN)-108/U, p. 20 11) M. Bormann, H. Neuert and W. Scobel, in Handbook on nuclear activation cross sections, IAEA Technical Reports Series No 156, Vienna, 1974 12) M. Herman, A. Marcinkowski and K. Stankiewicz, Nucl. Phys. A430 (1984) 69; A435 (1985) 859(E) 13) R. Bonetti, M. Camnasio, L. Colli Milazzo and P.E. Hodgson, Phys. Rev. C24 (1981) 71

A. Marcinkowski

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105

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