Calculation of Neutron Cross Sections on Isotopes of Yttrium and Zirconium

Home , Isotopes of yttrium, Isotope (catamaran)

pp. LA-7789-MS Informal Report

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LOS ALAMOS SCIENTIFIC LABORATORY Rpst Office Bex 1663 Los Alamos. New Mexico 37545 A LA-7789-MS Informal Report UC-34c Issued: April 1979

Calculation of Neutron Cross Sections on Isotopes of Yttrium and Zirconium

E. D. Arthur

- NOTICE- Tim report wt piepited u an account of work sponsored by the United Stales Government. Neither the United States nor the United Statci Department of Energy, nor any of their empioyeet, nor any of their contractor*, subcontractor!, or their employees, nukes any warranty, express or implied, ot astumes any legal liability 01 responsibility foi the accuiacy, completeness or luefulnets of any Information, apparatus, product or piocett ductoied.oi ^presents that iti uie would not infringe privately owned rights. CALCULATION OF NEUTRON CROSS SECTIONS ON ISOTOPES OF YTTRIUM AND ZIRCONIUM

E. D. Arthur

ABSTRACT

Multistep Hauser-Feshbach calculations with preequilibrium corrections have been made for neutron-induced reactions on yttrium and zirconium isotopes between 0.001 and 20 MeV. Recent- ly new neutron cross-section data have been measured for unstable isotopes of these elements. These data, along with results from charged-particle simulation of neutron reactions, provide unique opportunities under which to test nuclear-model techniques and parameters in this mass region. We have performed a complete and consistent analysis of varied neutron reaction types using input parameters determined independently from additional neutron and charged-particle data. The overall agreement between our calculations and a wide variety of experimental results available for these nuclei leads to increased confidence in calculated cross sections made where data are incomplete or lacking.

I. INTRODUCTION Neutron-induced cross sections on yttrium and zirconium isotopes are of interest because of their use as dosimetry reactions for various practical appli- cations. In addition to stable isotope data, there now exist experimental measurements for 14-15 MeV neutron reactions on certain unstable yttrium and zirconium isotopes. The comparison of these data and nuclear-model calculations can provide useful information regarding calculational techniques and input parameter values. Since there is an increasing trend to rely upon nuclear~model calculations to satisfy data needs for neutron-induced reactions in energy regions where measurements are incomplete or lacking, these types of comparisons become even more valuable. In addition, the proximity of these nuclei to the closed neutron shall at N = 50 leads to conditions arising from shell effects, separation energy differences, etc., which provide unique tests of nuclear models and which may allow information to be obtained that otherwise would be obscured. 1 In addition to direct measurements of neutron-induced reactions on unstable nuclei in this mass region, there are experimental data concerning proton-production cross sections that have recently become available through the use of charged-particle simulation reactions. Generally in medium-mass nuclei where competition between neutron and charged-particle reactions exists, neutron emission dominates, and there is a decreased sensitivity to the charged-particle parameters needed in a statistical calculation of the Hauser-Feshbach type. How- go QQ ever for Y(n,np) and Zr(n,np) reactions, proton emission occurs from compound systems where the proton binding energy is considerably lower than that of the 89 90 neutron. For example, in the Y and Zr compound systems, the proton binding energies are, respectively, 4.4 and 3.6 MeV less than those of the neutron. Thus, above the (n,np) threshold there is an energy region in which only proton and gamma rays compete with each other. In these cases, once parameters have been determined to describe gamma-ray emission, one has a unique situation in which to test proton optical parameters, especially their behavior at low-emission energies. We therefore describe calculations of neutron-induced reactions on yttrium and zirconium isotopes made using multistep Hauser-Feshbach techniques with corrections applied for nonstatistical effects through use of the exciton preequilib- 2 rium model. Realistic optical parameters were used for neutron emission, and gamma-ray emission was described with gamma-ray strength functions derived from neutron capture data for A = 80 to 99. Finally, proton optical parameters have been determined using, as a basis, recent results from sub-Coulomb barrier (p,n) 3 data modified somewhat to reproduce in the best possible manner (n,np) data available for yttrium and zirconium isotopes. Calculations are given for capture, total inelastic, (n,p), (n,a +n,an), (n,xn), (n,np + n,pn) and (n,noj) cross sec- 86—92 88—90 tions in the energy range from 0.001 to 20 MeV for the Y and Zr isotopes. In addition, cross sections for reactions leading to isomeric states having lifetimes greater than a millisecond were calculated. [Exceptions were isomeric cross sections resulting from (n,Y), Cn,a), and (n,not) reactions.]

II. MODEL CALCULATIONS AND PARAMETERS 4 5 The present calculations were made using the COMNUC and GNASH nuclear- model codes, both of which employ Hauser-Feshbach statistical model techniques to determine cross sections. The COMNUC code was used for incident energies up to 4 MeV since it includes width-fluctuation and correlation corrections important at lower energies. The GNASH program was used between 4 and 20 MeV. Tt allows decay of up to ten compound nuclei, with each decaying system permitted to emit gamma rays and up to five additional particles. The program includes preequilibrium emission and a complete treatment of gamma-ray cascades. In order to use these codecs properly, it is necessary to have the best information available concerning various input parameters. The remainder of this section deals with these model parameters and their determination in the most accurate manner possible.

A. Neutron Optical Parameters Neutron-transmission coefficients were calculated using optical parameters based on values determined from fits to neutron total cross sections, elastic- 89 6 scattering angular distributions, and resonance parameters for Y by Lagrange. Two changes were made to the parameters of Ref. 6. The real and imaginary potential depths were modified to include an (N-Z)/A dependence using values similar to those of Delaroche. Secondly, after preliminary Hauser-Feshbach calculations were made, it was felt that better agreement with experimental data [particularly (n,2n) cross sections] could be obtained if the total reaction cross section was increased a small amount for neutron energies above 10 MeV. The imaginary potential depth was increased slightly to achieve this with no noticable worsen- ing of the agreement with the total cross section. For zirconium isotopes the 89 real potential depth derived from fits to Y data was modified to improve agree- 90 ment with resonance parameter data while maintaining agreement with the n + Zr total cross section. The present parameters, given in Table I, provide reasonable transmission coefficients over the energy range from 0.010 to 20 MeV. Table II compares calculated and experimental resonance parameter data, while Fig. 1 on QA illustrates the agreement between calculated and experimental Y and Zr total cross sections.

B. Proton Optical Parameters The ability to accurately calculate (n,np) cross sections, especially near threshold, depends strongly on the proton transmission coefficients used, since most of the cross-section results from transitions to discrete levels in the residual nucleus and level-density effects are minimal. In cases where only gamma- ray emission competes, there is an additional sensitivity to the behavior of low- energy proton transmission coefficients. Recently results have been published

3 TABLE I

NEUTRON PARAMETERS USED IN THIS WORK V Isotopes r(fni) a(fm) V (MeV) = 53.21 - 30 (N-Z)/A - 0.28E 1.24 0.62 W (MeV) = 8.96 - 35 (N-Z)/A + C.3E 1.26 0.58 W (Maximum) = 7.0 - 7.5 MeV V = 6.2 MeV 1.12 0.47

Zr Isotopes

90Zr V(MeV) = 49.0 - 0.28E 1.24 0.62 W (MeV) = 3.4 + 0.3E 1.26 0.58 W (Maximum) =7.0 MeV V - = 6.2 MeV 1.12 0.47

88 89 ' Zr 90 Same as for Zr except V = 47.5 - 0.28E. (By making this change, the expected s- and p-wave strength values based on systematics were better reproduced.)

TABLE II

CALCULATED AND EXPERIMENTAL RESONANCE DATA

n + Y Calculation Experimental 0.47 0.28-0.32 S0 3.4 2.6-4.4 Sl R? 6.78 ^ 6.7

n + 9°Zr Calculation Experimental 0.466 0.56-0.62 S0 Sl 3.8 % 3.8 6.71 * 7.1 CROSS SECTION, BARNS CXTO aO 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 so (a r» —OP-1 1_ L ii.. «! H o CROSS SECTION, BARNS fi> 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 OJ 3 1 3 (t> 1 O. rt H« rt>CO o- OM vJ N O ^° U* >-« o H> H rt O

MUT R rt CO . °« *i ID ID H- O X o do 13 rt • z zS- » 3 o rt D> ft> M O s • W c (D (B CO rt C (D M O- rt CO s5 M, H* o r3t*

) by Johnson et al. dealing with optical parameters for sub-Coulomb barrier protons determined from the analysis of low-energy (p,n) reactions. In these analyses it was necessary to decrease the surface-derivative imaginary well depth to approximately one third of its usual value as obtained from conventional analyses of proton elastic-scattering data. This decrease qualitatively agreed with re- ft suits of fits to other low-energy proton data. We therefore used the Johnson parameters as a starting point for the determination of proton parameters used in this paper. The Johnson parameters were adjusted to produce agreement between calculated 89 87 and experimental Y(p,n) and Sr(p,n) cross sections when the modified Lagrange parameters of Sec. II. A were employed for the outgoing neutron channel. This differed somewhat from the calculation of Ref. 4, since there the Wilmore-Hodgson 9 neutron parameters were used. (We believe the modified Lagrange parameters to be superior to those of Wilmore-Hodgson, especially for the case of low-energy neutron emission.) Some adjustment was also made on the basis of preliminary an Hauser-Feshbach calculations of the Y(n,np) cross section. Table III lists the proton parameters of the present calculations. A main feature is the relatively small imaginary well depth. As noted before, Johnson and others have found it necessary to reduce the imaginary potential depth from about 13 MeV to about 4 MeV for low-energy protons. The strong energy dependence of the present imaginary potential ensures that for proton energies of 10-15 MeV, the imaginary potential well depth is around 12-14 MeV, in agreement with more conventional proton param- 10 eter sets. Figure 2 compares the reaction cross section calculated with the present parameters (solid curve) with values determined from several other proton parameter sets. The Johnson parameter results are indicated by the dashed line. The reaction cross sections calculated with the present parameters (Table III) agree reasonably with the Johnson results at low energies. At energies around 10-12 MeV, the reaction cross section obtained with the Johnson set does not increase with energy but instead^ s'hgws. a slight 'decrease. This is probably due in part to the fact that these parameters were determined from low-energy • • • data and do not have an imaginary potential energy dependence appropriate to describe higher-energy regions. The tr-iangles and circles result from calculations using the Perey optical parameters and the set of Schulte et al. The Perey parameters are a global set determined from the analysis of proton data in the mass range 30 ** A ^ 100 for energies < 20 MeV. The Schulte parameters were deter- OO OQ Qrt QO mined from fits to elastic scattering data on Sr, Y, Zr, and Mo in the TABLE III PROTON OPTICAL PARAMETERS

r ( fitp a(fm) V (MeV) = 56.4 + 24 (N-Z)/A + O.4Z/A ' - O.32E l\2_ 0.68 6E WSD (^eV) = 3' °' 1.225- .0.4 V =6.4 MeV 1.03 0.63

p + Y 1/3 V (MeV) = 56.4 + 24 (N-Z)/A + 0.4Z/A ' - O.32E 1.2 0.73 5E WSD °* 1.3 0.4 =6.4 MeV 1.03 0.63

in in o o •z.0.01 r o oJ- or 0.001 2 3 4 5 6 7 8 9 10 I! 12 13 14 15 16 PROTON ENERGY (MeV)

Fig. 2. 8g Calculated reaction cross sections for p + Sr. The solid curve results from the parameters of Table III, the dashed curve from the Johnson parameters,3 the triangles from the Perey and the circles are calculated with the Schulte parameters. energy range 8-14 MeV. Figure 2 shows that the parameters of Table III agree with the Johnson results at low energies while also agreeing with the other more conventional sets at higher energies. In Fig. 3 we compare (p,n) cross sections calculated using our proton param- D 89 89 eters (Table III) and neutron parameters (Table I) to the Y(p,n) Zr data of 3 Johnson et al. (Resonances have been omitted to facilitate comparison with the present Hauser-Feshbach statistical calculation.) Also indicated by the squares 12 are early (1951) measurements by Blaser et al. 88 89 87 88 For the calculation of ' Y(n,np) * Sr cross sections, experimental in- p "7 QO formation concerning ' Sr(p,n) reactions is of interest to provide a further check on our parameter sets. To our knowledge, the only published data for 87 88 1 9 ' Sr(p,n) reactions are the 1951 measurements of Blaser. Our calculation agrees well with these data as shown in Fig. 4. Even though these data are quite 89 old, the fact that the Blaser measurement for Y(p,n) agrees with the more recent Johnson results increases our confidence in its use for present proton-parameter determinations.

C. Gamma-Ray Emission Parameters Certain portions of our calculated results are sensitive to the description of gamma-ray emission, and therefore an accurate knowledge of the parameters involved is a necessity. In most Hauser-Feshbach calculations, the integral of the product of level density and gamma-ray transmission coefficients is normalized to the experimental value of 2u/, where and are the average gamma width and spacing for s-wave neutron resonances. This normalization directly influences the amount of gamma-ray emission occuring, either in the capture reaction or in competition to particle-emission reactions. Experimental data for and are not always reliable (especially where resonance spacings are large), and for compound systems lacking such data, reliance must be placed upon determination of these quantities from systematics. Since the observed spacing can vary drastically between nearby nuclei in closed shell regions, considerable uncertainty can exist concerning the amount of gamma-ray emission to be included in a calculation. 13 An alternate approach has been suggested by Gardner that elimiates many of these problems, leading in turn to more accurate capture cross sections where data is unavailable and to a better treatment of gamma-ray competition. This method is based upon determination of the gamma-ray strength function f(e ) defined by o

PROTON ENERGY (MeV) 3. 89 The calculated Y(p,n) cross section is compared to the data of Johnson^ (circles) and Blasser^ (squares).

3 4 S fi 7 PROTON ENERGY (MeV)

87 Calculation of the Sr(p,n) reaction is compared to the Blasser data.12

where S is the neutron separation energy and p is the level density of the compound system. The electric dipole strength function is assumed to have a giant dipole resonance (GDR) form given by

k£ r * ,F. \ = Y GDR m 2 2 2 u; + (£ E )V ' Y " GDR

The strength function can be extracted from the analysis of neutron capture cross sections measured for stable nuclei or through the analysis of spectral data resulting from capture. Since the strength function is expected to vary smoothly between nearby nuclei, some of the problems mentioned earlier can be eliminated, and one can use it with increased confidence. Prior to the present calculations, we explored the magnitude and behavior of these strength functions by fitting neutron capture cross sections to obtain 80 99 values for the constant k in Eq. (2) for target nuclei from Se to Tc. We considered only El contributions and took the giant dipole resonance parameters rnm> and Err>D from photonuclear data. The El strength functions for several compound systems are shown in Fig. 5. 85 87 90-92 We concluded from the analysis of ' Rb(n,Y) and Zr(n,Y) data that the strength function was almost identical (within the accuracy of our fit) for 89 91 92 isotopes of the same element. The strength functions for Sr and ' Zr com- 90 pound systems lie very close to the values for Y and, for clarity, have been oo omitted in Fig. 5. Since recent experimental results are available for the Sr, 89 90-92 15—17 Y, and Zr(n,Y) reactions, we believe the extracted strength functions to be particularly reliable for these cases.

D. Level Density Parameters In the present calculations all nuclei are described using a combination of discrete levels and a continuum level-density expression at energies high enough 'where reliable experimental level data do not exist. We used the Gilbert-Cameron * 10 18 19 level density expression along with the Cook values for the pairing terms and level-density parameter, a. The Gilbert-Cameron formalism consists of a Fermi-gas level-density expression along with a constant-temperature expression of the form

(E-E.)/T U (3)

which represents the level density at lower-excitation energies. The Fermi-gas and constant-temperature expressions are then joined smoothly at a matching energy U . These expressions should also be joined smoothly to the cummulative number of discrete levels available from experimental data at lower energies. To do so, we adjusted E_ and T in Eq. (3) and the matching energy U until these conditions were met. At times it was also necessary to adjust the pairing energy used in the Fermi-gas expression from the values given by Cook. For some nuclei we chose values for the level-density constant a, which agreed with results from a more 20 recent and specialized analysis of resonance spacings in this mass region. Table IV lists the level density parameters used in the present calculations.

10 0.0 3.0 4.0 5.0 6.0 7.0 8.0 10.0 11.0 Gamma-Ray Energy (MeV) Fig. 5. Gamma-ray strength functions determined from fits to neutron capture data are presented for several compound nuclei.

11 TABLE IV LEVEL DENSITY PARAMETERS OF THE PRESENT CALCULATIONS

Nucleus (KeV"1) EQ(MeV) T(MeV) U (MeV) Rb82 12.802 0.29 -0.436 0.629 3.162 Rb83 12.669 1.61 -0.921 0.836 7.694 Rb84 12.313 -0.12 -0.385 0.773 0.163 Rb85 11.591 1.50 -0.262 0.816 6.475 Rb86 10.761 0.04 -0.312 0.663 2.36 Rb87 9.689 0.97 -0.053 0.843 4.927 Rb88 10.083 0.05 -0.945 0.812 3.880 Rb89 10.671 0.66 -0.315 0.773 4.355

Sr84 12.675 2.81 1.09 0.758 7.544 Sr85 12.312 1.08 -0.435 0.753 5.51 Sr86 11.589 2.7 0.987 0.812 7.595 Sr87 10.734 1.24 0.767 0.688 3.854 Sr88 9.00 2.17 1.812 0.921 7.437 Sr89 10.043 1.25 1.095 0.687 3.547 Sr90 10.634 1.86 1.252 0.719 4.809 Sr91 11.662 0.74 0.171 0.659 3.465 Sr92 11.756 2.66 0.975 0.802 7.511

85 y 12.452 1.86 -0.834 0.861 8.253 86 Y 12.078 0.13 -0.854 0.699 3.618 Y87 11.341 1.75 0.643 0.753 5.584 Y88 10.00 0.29 -0.764 0.826 4.253 Y89 9.365 1.22 1.181 0.821 5.303 90 Y 9.759 0.03 -0.262 0.766 3.291 Y91 10.352 0.91 0.338 0.73 3.83 Y92 11.385 -0.21 0.142 0.804 0.088 Y93 11.475 1.71 -0.383 0.873 6.404

Zr87 12.585 0.93 0.763 0.539 2.575 Zr88 11.0 2.55 0.815 0.848 7.597 Zr89 10.965 1.09 0.133 0.753 4.701 Zr90 9.85 2.02 1.157 1.092 2.35 Zr91 10.252 1.10 0.669 0.853 1.46

The quantities above are defined as follows: a = Level density parameter appearing in the Fermi-gas level density expressions. A - Pairing energy. E. and T • Constant temperature expression parameters. See Eq. (3). U » Matching energy at which constant temperature and Fermi-gas expressions are joined.

12 E. Discrete Levels In some cases discrete-level information plays an important role regarding cross sections determined for (n,2n) or (n,np) reactions. For example, the difference in spins populated in the initial compound system and that of the residual nucleus reached through decay via neutron or proton emission can lead to cross sections dominated by populations of one or a few levels. Near thresholds, the importance of accurate discrete-level information is increased because of the absence or lack of significant population of states in the continuum represented by a level-density expression. We made an effort to include as many levels as possible and to, of course, make the best judgment possible for spin and parity values where such information was incomplete. Information from the latest evalu- 21 ations and compilations appearing in the Nuclear Data Tables formed the basis for the majority of the level schemes used. However, in some cases it was necessary to make judgments based on newer experimental data or from systematics. The level schemes used in this report appear in Appendix A.

F. Preequilibrium Formalism and Parameters At higher neutron energies, effects other than those included in the standard Hauser-Feshbach statistical calculation become important. These semi-direct effects result from the reaction proceeding through a series of particle-hole configurations, starting from very simple ones and l'eading to more complex ones until equilibrium is reached. At each successive stage there exists a probabil- ity for particle emission, and the resultant spectra and cross sections can be quite different from those obtained from Hau^rrFeshbach methods. To describe the preequilibrium procesls, we have used the Kalbach exciton model of Ref. 2. Since the expressions used to calculate preequilibrium contributions are given in detail there, we will no% repeat them. However in such calculations, state densities are used to classify the number of particle-hole de- grees of freedom. Since the excitation energy of the system is redistributed through a series of two-body energy-conserving interactions, expressions describ- ing the rates for creation or destruction of particle-hole pairs are needed. Such rates are directly proportional to the square of the average matrix element W" for the effective, residual two-body interaction. In our present calculations 2 ° 22 we have used a new empirical representation for M developed by Kalbach

13 M2(n,E) = -y- f(e) , (4) A e '

where n is ..he exciton number (n = p + h) and e Is the average excitation energy per exciton, E/n. The function f(e) represents a different energy dependence 2 for M over several ranges of e and appears explicitly in Ref. 22. In Eq. (4) 3 the value of the constant k was determined to be 135 MeV when the state density constant for the composite system g was equal to A/13, where A is the nuclear 3 mass. We obtained better results wich k = 160 MeV when gQ = A/13. However, we chose to represent the state density constant for each residual nucleus g as g 6 = —„ a. where a is the level density constant of Sec. II. D. In this mass re-

gion, shell effects are important, and values of the level-density constant a deviate from values obtained from systematics in regions away from closed shells, namely, a ^ A/8. Since the excitation energies of the residual systems are relatively low, we concluded that shell effects may play some role in preequllibrium calculations. However, for the composite systems, the state density constant g. was retained equal to A/13 since at the higher-excitation energies involved, shell effects should be less noticable. Attempts to calculate preequilibrium components when all state density constants (including that of the composite system) were set equal to —_ a produced unusually high preequilibrium fractions IT for incident-neutron energies between 10 and 20 MeV. Over the same energy range, the preequilibrium fraction calculated using the state density constants described above ranged from 15-30%. We also included pairing effects in the determination of the energy at which the state density was to be evaluated. To include nonstatistical effects occuring in the emission of complex particles (namely, alpha particles), we employed semiempirical expressions developed 3 23 by Kalbach ' to describe knockout and inelastic processes as well as stripping and pickup. These expressions made it unnecessary to use quantities such as "alpha preformation" coefficients, and in general the method worked reasonably well. For alpha emission, the dominate contribution originates from pickup and knockout and not from statistical or purely preequilibrium processes. Finally, since the exciton model used here does not include angular momentum effects, we assumed that the spin distribution of the preequilibrium components would be the same as those determined for the equilibrium components through the usual Hauser-Feshbach techniques.

14 III. CROSS SECTION RESULTS In this section we compare cross sections calculated using the techniques and parameters of Sec. II with available experimental data. Trends in cross sections for different isotopes of yttrium and zirconium will also be illustrated.

Table V lists.t the reactions calculated, their threshold, and the reaction type (MT) numbers as used in the ENDF/B system for evaluated neutron data. For all reactions [except capture and (n,a)], cross sections for production of isomeric levels having lifetimes roughly a millisecond or greater were calculated. In ac- cordance with procedures for the ENDF/B system, we have provided cross sections from the reaction threshold up to 20 MeV. For reactions having positive Q values, cross sections begin at 10 eV and extend to 20 MeV. In these cases, we used the nuclear model calculations over the energy range generally from 1 keV to 2Q MeV. From 10~ eV to 1 keV, cross-section estimates were made based on knowledge of thermal values and expected resonance locations. The method used for esti- mating cross sections below the lower limit for statistical calculations and the complete cross-saction sets appear in Appendices B and C.

A. Yttrium Results and Comparisons to Experimental Data 1. Elastic and (n,n') Cross Sections. Althoush these cross sections are 89 not provided in Appendix C, the calculated results for the Y elastic cross section and inelastic scattering to specific final states are compared to the data 24 of Perey and Kinney in Figs. 6 and 7. The generally good agreement between the calculations and data is indicative of the applicability of the neutron optical parameters used in the present calculations. 25—29 89 There also exist several measurements of the Y(n,n') reaction leading 89 ^ + to the 16 second isomer in Y (E = 0.909 MeV, J = 9/2 ). These results span the region from 2-18 MeV and are compared to our calculated values in Fig. 8. These data, which cover a wide energy range, provide a useful test of our calculations, particularly with respect to the treatment of gamma-ray cascades instru- mental in the population of this state at higher energies and in the preequilibrium corrections used. The preequilibrium contributions prevent the calculated cross sections from dropping to zero once thresholds for tertiary reactions occur. 2S Reasonable agreement is obtained with the higher-energy data of Abboud (circles). Another test of preequilibrium cross sctions occurs through the comparison shown in Fig. 9. Here the secondary neutron-energy spectrum measured by Luk'- 30 yanov for an incident energy of 14.36 MeV is compared to our calculated

15 TABLE V Q-VALUES AND THRESHOLDS FOR YTTRIUM AND ZIRCONIUM REACTIONS

Final Q Et MAT MT Reaction Statea (MeV) (Me

3986 4 86Y(n,n')86Y 0 16 86Y(n,2n)85Y 0 16 86Y(n,2n)85mY 1 22 Y(n,na)°^Rb 0 28 86Y(n,np + i,pn)85Sr 0 52 86Y(n,n')86nV 2 86 87 102 Y(n>Y) Y 0 11.82 — 103 Y(n,p)°°Sr 0 6.055 107 Y(n,a + n,an) » Rb 0 5.359 —

87 87 3987 4 Y(n,n') Y 0 - 3.81 0.386 16 87Y(n,2n)8bY 0 -11.82 11.96 16 87Y(n,2n)86mY 2 -12.04 12.17 22 87Y(n,na)83Rb 0 - 6.46 6.535 28 87Y(n,np + n,pn)86Sr 0 -5.764 5.831 51 87Y(n,n')87mY 1 - 3.81 0.386 102 87Y(n,y)88Y 0 9.377 - 103 87Y(n,p)87Sr 0 2.665 103 87Y(n,p)87mSr 1 2.276 ~ 107 87Y(n,a + n,an)84'83Rb 0 2.416 88 88 3988 4 Y(n,nf) Y 0 - 0.232 0.235 88 87 16 Y(n,2n) Y 0 - 9.376 9.484 16 88Y(n,2n)87"V 1 - 9.758 9.87 88 8 h 22 Y(n,na) Rb 0 - 3.73 3.773 88 87 28 Y(n,np + n,pn) Sr 0 - 6.712 6.789 88 87m 28 Y(n,np + n,pn) Sr 1 - 7.1 7.182 52 88Y(n,n')88mlY 2 - 0.393 0.398 53 88Y(n,n')88m2Y 3 - 0.675 0.683 102 88Y(n,y)89Y 0 11.468 103 88Y(n,p)88Sr 0 4.401 16 88 85 84 107 Y(n,a + n,an) ' Rb 0 3.517 3989 / 89Y(n,n')89Y 0 - 0.908 0.918 T 16 89Y(n,2n)88Y 0 -11.468 11.598 16 89Y(n.2n)88mlY 2 -11.86 11.96 16 89Y(n,2n)88m2Y 3 -12.143 12.281 22 89Y(n,na)85Rb 0 - 7.95 8.04 QQ QO 28 0 - 7.07 7.147 Y(n,np + n,pn) Sr 51 1 - 9.08 0.918 89Y(n,n')89mY 102 0 6.86 89 9 Y(n,Y) °Y 102 89Y(n,T)90nV 2 6.178 — 103 89Y(n,p)89Sr 0 - 0.707 0.715 107 Y(n,a + n,an) 0 0.699 —

3990 4 9°Y(n,n.)9°Y 0 - 0.203 0.205 16 9°Y(n,2n)89Y 0 - 6.86 6.937 16 9°Y(n,2n)8% 1 - 7.768 /.855 17 9°Y(n,3n)88Y 0 -18.33 18.53 22 9°Y(n,na)86Rb 0 - 6.16 6.23 QO ftQ 0 7.567 7.652 28 Y(n,np + n,pn) Sr 52 90Y(n,n')90^/ 2 - 0.685 0.693 102 9°Y(n,Y)91Y 0 7.946 — 9 9 103 °Y(n,P) °Sr 0 0.237 107 90Y(n,a + n,an)87'86Rb 0 3.765

3991 4 91Y(n.n')91Y 0 - 0.556 0.562 16 91Y(n,2n)9°Y 0 - 7.946 8.034 16 91Y(n,2n)9(N 2 - 8.63 8.727 17 91Y(n,3n)89Y 0 -14.81 14.97 17 91Y(n,3n)8% 1 -15.71 15.89 22 Y(n,na) Rb 0 - 4.18 4.23 91 , , .90,, 28 Y(n,nTr p + n,pn) Sr 0 - 7.709 7.759 51 91Y(n,n')9^ 1 - 0.556 0.562 102 91Y(n,Y)92Y 0 6.557 — 103 91Y(n,p)91Sr 0 - 1.883 1.903 107 91Y(n,a + n,an)88)87Rb 0 1.902

92 92 3992 - 0.28 0.283 17 3992 16 92Y(n,2n)91mY 1 - 7.113 7.191 17 92Y(n,3n)9°Y 0 -14.5 14.66 17 92Y(n,3n)9OmY 2 -15.19 15.35 „ o "o 22 92Y(n,na)88Rb 0 - 4.655 4.706 28 92Y(n,np + n,pn)91Sr 0 - 8.44 8.532 102 92Y(n,Y) Y1' 0 7.49 103 92Y(n,p)92Sr 0 - 1.13 1.14 ,107 92Y(n,a + n,an)89>88Rb 0 2.52

4088 4 88Zr(n,n')88Zr 0 - 1.058 1.07 16 88Zr(n,2n)87Zr 0 -12.2 12.34 16 88Zr(n,2n)87mZr 2 -12.536 12.68 22 88Zr(n,na)84Sr 0 - 5.397 5.449 28 88Zr(n,np + n,pn)87Y 0 - 7.917 8.01 88 87m 28 Zr(n4np + n,pn) Y 1 - 8.298 8.39 102 88Zr(n,Y)89Zr 0 9.312 103 88Zr(n,p)88Y 0 1.462 103 88Zr(n,p)88mlY 2 1.069 103 88Zr(n,p)88m2Y 3 0.787 107 88Zr(n,a + n,an)85'84Sr 0 3.13 —

4089 4 89Zr(n,n')89Zr 0 - 0.587 0.594 16 89Zr(n,2n)88Zr 0 - 9.311 9.417 22 89Zr(n,na)85Sr 0 - 6.18 6.25 28 89Zr(n,np + n,pn)88Y 0 - 7.853 7.941 28 89Zr(n,np + n,pn)88mlY 2 - 8.245 8.339 89 88m2 28 Zr(n,nP + n,pn) Y 3 - 8.527 8.624 51 89Zr(n,n')89mZr 1 - 0.587 0.594

89 9 102 Zr(n,Y) °Zr 0 11.983 103 89Zr(n,p)89Y 0 3.616 — 103 89Zr(n,p)89mY 1 2.708 107 89Zr(n,a + n,an)86>85Sr 0 5.305 —

4090 4 Zr(n,nf) Zr 0 - 1.76 1.78 on RQ 16 Zr(n,2n) Zr 0 -11.^3 12.117

16 9°Zr(n,2n)89mZr 1 -12.57 12.71

18 90 86 4090 22 Zr(n,n ) Sr 0 - 6.678 6.753 an on 28 Zr(n,np + n.pn) Y 0 . - 8.366 8.46 28 Zr(n,np + n,pn) aY 1 - 9.27 9.38 90, , ,91 Zr(n, ) Zr 0 7.203 — 103 9°Zr(n,p)9°Y 0 - 1.506 1.523 9 9( 103 °Zr(n,P) N 2 - 2.19 2.216 107 Zr(n, + n, n) ' Sr 0 1.75

The convention used here is that for a particular reaction a final state of 0 signifies that the cross section listed is the total cross section for that reaction, not just the amount leading to the ground state. If the final state is not equal to 0, then the cross section listed is that for population of the indicated isomeric stat^.

ELASTIC 10" 1 IO E,'{2.53O*2.5T0*2.63O)HiV

10'

t,-(2.880*2.890) MiV ~ IO2 o H U UJ en to co I0 O ID o o IOZ o 10'

E. •(3.720*3.760+3.860 3.S?0)N«Y

10' O I 23456789 0 I 23456789 NEUTRON ENERGY (MeV) NEUTRON ENERGY {MeV)

Fig. 6. Fig. 7. Calculated elastic and inelastic excita- Further comparison of the calculated tion functions for n + 8^Y are compared yttrium inelastic scattering cross sec- to the data of Perey and Kinney.24 tions to the Perey results.24 19 4 6 8 10 12 14 16 18 20 NEUTRON ENERGY (MeV)

Fig. 8. g. Calculated and experimental cross sections for the production of T through neutron inelastic scattering (the data of Refs. 25-29 are o , V » A > A > and n , respectively).

n *89Y-NEUTRON EMISSION En = 14.36 ±.!5 MeV

•10

o o

I01

6 2 4 6 8 10 12 SECONDARY NEUTRON ENERGY (MeV) Fig. 9. The calculated secondary neutron emission spectra at 14.36 MeV is compared to the Luk'yanov data.30

20 spectrum. The fact that reasonable agreement is obtained, especially for secondary energies greater than 6 or 7 MeV, indicates the use of a proper fraction

in the preequilibrium correction. c 2. (n,2n) Cross Sections. Various experimental measurements exist for the pQ QQ Y(n,2n) Y reaction. In Fig. 10 we compare our calculations to three of the most recent. The closed circles are the scintillation tank measurements of Frehaut from threshold up to about 15 MeV, while the open circles are the Veeser 32 results (also scintillation tank measurements). The triangles are data of Bay- 33 hurst et al. measured using activation techniques. Good agreement is obtained between calculated and experimental results, even near the threshold. This indicates that a proper amount of gamma-ray competition has been included using the strength functions described in Sec. II. C. It also provides an indirect confir- 89 mation that the amount of competition from the Y(n,np) reaction is reasonable for energies less than 13-14 MeV. 34-37 A few experimental results exist for population of the first and second isomeric states in Y(E = 0.393 MeV, J71 = 1+, and E = 0.687, JU = 8+) through the Y(n,2n) reaction. Our results are shown in Fig. 11 with these data (closed symbols art experimental cross sections for production of the first isomeric state, while the open ones are results leading to the second). Our calculations for the first isomer do rather poorly in reproducing the data, while for the second, the scatter in the experimental data prevent a firm conclusion although perhaps the agreement is somewhat better. 38 Recently, experimental measurements of the (n,2n) cross section for neu- 88 trons incident on the unstable Y nucleus have been made. Although these data generally exist at only one energy around 14.7 MeV, they provide a unique test of nuclear-model calculations in regions where one has to rely increasingly on parameters determined from systematics. Figure 12 shows data for the Y(n,2n) reaction, both for the total (n,2n) cross section (open circles) and that (closed 87 + circles) leading to the Y isomeric state at E = 0.381 MeV (J71^ = 9/2 ) alone 88 x with our calculations. The Y(n,2n) cross section is somewhat higher at 14 MeV 89 than that for the Y(n,2n) reaction as a result of a lower threshold and a decreased competition from charged-particle emission. 3. (n,p) and Proton Production Cross Sections. The proton optical model- parameters we have used represent a departure from values generally employed in Hauser-Feshbach calculations. In Sec. II. C we showed that (p,n) cross sections calculated with these parameters sets agreed with experimental data for Y and 21 12 13 14 15 16 17 18 20 NEUTRON ENERGY(MeV)

89 Fig. 10. The calculated Y(n,2n) cross section is compared to three recent experimental data sets ( • Ref. 31, A Ref. 32, and o Ref. 33).

0.35 • 89Y(n,2n)88lril-m2Y

12 14 16 18 20 NEUTRON ENERGY (MeV)

88 89 Isomeric state yields in Y from the Y(n,2n) reaction. The closed symbols are 89III1Y results while the open symbols are 88m2Y data (AARef. 34,VTRef. 35, • Ref. 36, and o» Ref. 37). 22 10 12 14 16 18 20 NEUTRON ENERGY (MeV)

Fig. 12. „_ Calculated cross sections for the eoY(n,2n) reaction are compared to the data of Ref. 38.

87 Sr(p,n) reactions. Our main interest, however, is knowing to what extent these parameters (along with those developed for neutron and gamma-ray emission) produce cross sections that agree with data for proton production induced by neutrons on isotopes of yttrium. Until recently, the only available proton emission cross-section data available for yttrium were activation measurements of the 89 .89,, 89 Y(n,p; Sr cross section. Since the Y(n,np + n,pn) reactions lead to the QQ stable Sr nucleus, there have been no data pertaining to this cross section. This situation has changed as a result of recent data from charged- particle reactions that simulate proton production arising from neutron-induced reactions on yttrium isotopes. For example, proton emission resulting from n + Y is simulated through use of the Zr(t,a) reaction, which produces 9°Y in a series of excited, unbound states. By measuring the proton emission probabil- ity and normalizing it with a calculated compound-nucleus formation cross section, the total proton production cross section can be determined for an equivalent neutron energy. Before comparisons are made to this type of data, Fig. 13 shows our calcu- 89 40-44 lated Y(n,p) cross section along with available experimental data. With the proton parameters of Sec. II. C, reasonable agreement is obtained between the calculation and data, especially for energies greater than 14 MeV. The total proton production cross section measured through charged-particle 89 simulation of the n + Y -*• p + X reactions is compared with our calculation [sum of contributions from (n,p) + (n,np) + (n,pn)] in Fig. 14. The experimental data show a rapid rise above 10 MeV, which corresponds to the excitation energy region 89 in the Y compound system where only proton and gamma-ray emission occur. Once neutron emission begins, the proton production cross section drops. In the equiv- 89 alent n + Y calculations, the (n,np) reaction is the major contributor to the peak around 12.5 MeV. Competition from the (n,2n) reaction causes the proton production to then drop at higher energies. Although all points in the measured data are not reproduced, the calculated values agree well with the main features. on Similar measurements exist for the n + Y •*• p + X reactions and are shown in Fig. 15. Here the calculations fail to reproduce some of the features, particularly the measured rise around a neutron energy of 8 MeV. Even though the threshold for the (n,np) reaction is 6.79 MeV, Coulomb barrier effects prevent sizable contributions to the calculated cross section until 10 MeV. Using similar proton parameters as those used in the curve appearing in Fig. 14, the general magnitude of the cross section is reproduced however. 45-54 89 4. The (n,Y) Cross Section. Experimental data exist for the Y(n,Y) cross section over a wide energy range extending from approximately 100 e\> to 15 89 MeV. We fitted the Y(n,Y) experimental data for energies between 0.01 and 0.5 MeV to extract the El gamma-ray strength function for yttrium isotopes, and our calculation is compared to the data in Fig. 16. (Below 7 keV the curve was sim- 45 ply hand-drawn through the data of Bergman for the purpose of providing an evaluation of this cross section.) Above 7 keV and extending to approximately 10 MeV, the curve results from our Hauser-Feshbach calculation of the capture cross section. In the region from 10-20 MeV, we calculated the cross section using a semiempirical model to simulate the direct-semidirect processes through which the El giant dipole resonance influences the capture cross section. In this model, the cross section was calculated using a preequilibriutn cascade process with gamma-ray emission probabilities computed at each stage. The calculations ex- hibit a giant dipole resonance effect, and for energies around 14 MeV the cross

sectio n 55is around 1-2 mb in agreement with measured values for a wide range of nuclei-. A . 24 \ 'I •i

O 0.01 UJ c/) in c/> 89Y(n,p)89Sr O a: o

o.ooi 6 8 10 12 14 16 18 20 NEUTRON ENERGY (MeV)

Fig. 13. 89. Calculated and experimental data for the Y(n,p) reaction (A Ref. 40, C Ref. 41, D Ref. 43,V Ref. 44, and • Ref. 45).

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 NEUTRON ENERSY(MeV)

Fig. 14. 89 Calculated total proton production cross section for n + TY compared to the results from charged-particle simulation of this reaction.39

25 0.12 i i r i 9°Zr(t,a)8V 88 0.10 (n+ Y-p*x)

-- 0.08 O h O 06

$0 04 O °0.02

J I 0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 NEUTRON ENERGY(MeV)

Fig. 15. 88. Calculated total proton production cross section for n + compared to the results from charged-particle simulation of this reaction.

~1 1 I I I I ll| f 1—I IIII1| 1 1 1 I I I ll| 1 1 I I I I ll|

0.100 89 90 Y(n,y) Y

0.001 -

i i i i i t 111 i i i I i i 111 i i (Mini 0.001 0.01 0.1 1.0 100 NEUTRON ENERGY (MeV)

Fig. 16. Experimental data for the 89Y(n,y) reaction are compared with our calculated (evaluated) results. (Data from Refs. 45-54 are represented by o , • , a , A , • , V , • , A , 0 , and # , respectively.)

26 5. (n,q) and Alpha Production Cross Sections• Alpha production cross sections generally are lower in magnitude than most other cross sections calculated here and are, thsrefore, of less interest. We included (n,a) and other alpha-production cross sections in the calculations, but a thorough investigation of alpha- particle optical parameters was not made. In addition, a large contribution to alpha production arises from nonstatistical effects described in Sec. II. F, and there is a decreased sensitivity to the alpha-particle transmission coefficients used. We chose the parameters of Park determindeterminei d from 20 MeV alpha scattering on yttrium for use throughout these calculations. 89 Adequate agreement was obtained for the calculated Y(n,c) cross section 40-43 cotapared to the experimental data as shown in Fig. 17. Since we did not separate the (n,a) and (n,an) cross sections in the calculation, the solid curve represents the contribution estimated to be largely from the (n,a) reaction, while the dashed portion includes both (n,a) and (n,an) contributions. Other comparisons made to the total alpha-production cross section as measured through 89 charged-particle simulation of n + Y^ot+X reactions also show good agreement.

B. Cross Section Trends for Yttrium Isotopes Here we compare trends in the cross sections determined for selected neutron 86—9? reactions on "Y. Figure 18 illustrates the capture cross sections. All QQ curves are calculated values except for the Y(n,Y) reaction below 7 keV where experimental information indicates the presence of a resonance. For the other yttrium isotopes, resonance effects should occur at lower energies since their 89 resonance spacing is expected to be less than that for the n + Y compound system (see Appendix B). Thus, Hauser-Feshbach calculations for these isotopes should be applicable for .1 kilovolt (and perhaps lower) incident-neutron energies. As we described in Sec. II. C, all capture calculations relied on use of the gamma- 89 ray strength function determined from Y(n,Y) data to provide a normalization for for the gamma-ray transmission coefficients used. At low energies, the capture 86-88 cross sections for Y are the largest since their neutron separation energies 89-92 are higher (9.4-11.8 MeV) than those for Y (6.6-7.9 MeV). Thus, the integral over the product of the normalized gamma-ray transmission coefficients and the compound nucleus level density extends over a larger integration range resulting in a larger capture cross section. At higher energies, the presence of the El giant dipole resonance (GDR) was incorporated in the manner described in Sec. III. A. 4. All capture cross sections have approximately the same magnitude around 15 MeV in

27 ^Ydi.oj^Rb

10 12 14 16 18 20 NEUTRON ENERGY (MeV)

Fig. 17. g9 Calculated and experimental data for the Y(n,a) reaction. The portion of the curve represented by a dashed line also includes the (n,an) contributions. Data are from Ref. 40 t 41 o , 42 • , and 43 V .

1 1 1

92 " Y(n y) 10

O.I NTS 0.01 \ 0.001

1 t . . . 1 0001 0.01 0.1 1.0 NEUTRON ENERGY (MeV) • Fig. 18, 86-92 Trends in calculated neutron capture cross spctions for Y.

28 agreement with expected trends arising from experimental data at this energy. In cases where the capture component resulting from compound-nucleus contributions is large ( Y), the giant dipole resonance shape is distorted on the low-energy side. For the other cases with relatively small compound-nucleus contributions, such effects are minimal. Figure 19 compares cross sections calculated for (n,2n) reactions on these isotopes. Several general characteristics are apparent. The neutron-rich iso- 90-92 topes Y have larger peak (n,2n) values, partially because of lower (< 8 MeV) 91 92 thresholds and less competition from charged-particle emission. For ' Y, the (n,3n) threshold occurs around 16 MeV, causing a decline in the (n,2n) cross sec- 86 87 tion above this energy. The proton-rich ' Y isotopes have more competition 86 from the (n,np) process therefore lowering the (n,2n) cross section. For Y, the effect is most apparent causing a substantial lowering of the cross section as well as influencing the shape of the excitation function. The calculated (n,p) cross sections are illustrated in Fig. 20. The proton- rich isotopes have positive Q values for this reaction, leading to appreciable 8fi cross sections at low energies. The Y(n,p) reaction has the most positive Q value (6.055 MeV) resulting in the largest (n,p) cross section at low energies and continuing up to 20 MeV. The structure in this cross section around 2-3 MeV occurs from a peaking in the calculated inelastic cross section resulting in a drop in the (n,p) cross section. At 3 MeV, the inelastic cross section begins 89 to drop, caut-lng the (n,p) cross section to rise again. The Y and neutron-rich 90-92 isotopes Y have r i tive Q values resulting in a threshold for this reaction and a smaller peak magnitude. Much of the behavior of the (n,np + n,pn) cross sections of Fig. 21 can be explained in terms of the difference in neutron and proton binding energies of 89 the second compound nucleus involved. As noted earlier for n + Y, the binding QQ energy of the proton in the Y compound system is 4.4 MeV less than that of the neutron leading to a peak around an incident energy of 12 MeV from the (n,np) 88 contribution. This situation occurs for the Y system but to a lesser extent. Here the difference in proton- and neutron-binding energies is approximately 2.7 MeV, and a shoulder occurs in the cross section. Again, the difference is large 86 87 90—9? for ' Y, resulting in a peak. For the Y isotopes, the binding energy of 90-92 the neutron in the Y compound systems is less than that of the proton and there is very little (n,np) contribution. In these cases most of the calculated cross section arises from the (n,pn) reaction. 29 1 1 1 1 1 1 !

1.5} _86-92Y(n2n)

1.25-

1.00-

/ 89/ / o £0.75

en 0.50- - o • H / 0.25- T

10 12 14 16 18 20 NEUTRON ENERGY (MeV)

FiS- 19- 86-92 Calculated (n,2n) cross sections for the Y iisotopes

0.001 0.01 0.1 10 10.0 NEUTRON ENERGY(MeV)

86-92. Fig. 20. Calculated Y(n,p) cross sections from 0.001 to 20 MeV.

30 o I- o LU

o it

001

0001 10 12 14 16 20 NEUTRON ENERGY (MeV)

Fig. 21. Sum of calculated (n,np) and (n,pn) cross sections for 86-92Yf

C. Cross Sections and Comparisons to Data for Zirconium Isotopes In this section we compare calculated and experimental cross sections for selected neutron reactions on zirconium isotopes. As was the case for yttrium, there also exist unstable isotope measurements for zirconium. These data supple- ment the unstable yttrium isotope results and place further constraints on the techniques and parameter values used to calculate theoretical cross sections in this mass region. 1. Inelastic Scattering Cross Sections. In Fig. 22 we compare our calculated cross section for production of the isomeric state (E = 2.319 MeV, J11 = 5 ) 90 x in Zr through inelastic neutron scattering. The calculations lie slightly 57 58 above the experimental data, ' but the agreement is reasonable. Unfortunately, the experimental data extend only to 6 MeV, preventing a test at higher energies as was the case for the Y(n,n') Y reaction. Similar information exists from measurements for production cross sections for discrete gamma-ray lines through 90 59 Zr inelastic neutron scattering. In Fig. 23 the data of Glickstein et al. are shown along with our calculations. All these gamma rays result from 31 8 10 12 14 16 18 20 NEUTRON ENERGY (MeV)

Fig* 22< 90 90m Calculated and experimental cross sections for the Zr(n,n ) Zr reaction (• Ref. 57, and • Ref. 58).

90 Zr(n,n'y) 02:

0.20

015

-~ 0.10

S 0.30

O £0.25 V) in O 0.20 o 0.20

015

0.10

4 5 6 3 4 5 6 NEUTRON ENERGY(MeV)

Fig. 23. Calculated results for discrete gamma rays following inelastic neutron 59 scattering on 90zr are compared with the data of Glickstein et al.

32 + 90 transition between discrete levels lying below the 2 level in Zr at 3.309 MeV. Further detail concerning these transitions can be found in Ref. 59. This comparison not only tests the population of states directly by inelastic scattering but also the population of levels through gamma-ray cascade processes. 2. (n,2n) Cross Sections. For this reaction a unique situation exists, be- 90 cause in addition to Zr(n,2n) results there are also experimental measurements QO QQ on the unstable ' Zr isotopes. Thus, neutron parameters that provide good 90 results for the Zr(n,2n) reaction can be tested to determine how well they reproduce the (n,2n) cross section on these unstable isotopes. The treatment of charged-particle competition and its influence on these cross sections can also be indirectly tested. Many experimental measurements ' ' of the Zr(n,2n) reaction exist, and six are shown with our calculated curve in Fig. 24. The calculations agree 33 quite well with the data, especially compared to the recent Bayhurst results (denoted by the V symbol). Also, a relative abundance of data ' ' ' for 89 TT — this reaction leading to the Zr isomeric state (E = 0.5M8 MeV, J = 1/2 ) exist. As seen in Fig. 25, the calculations agree well with the experimental data from threshold up to 18 MeV. 89 Comparatively speaking, the unstable Zr nucleus has a wealth of (n,2n) 72 data in that measurements have been made for 3 neutron energies between 14-15 MeV, giving valuable information concerning the shape of the (n,2n) excitation curve. Our calculation agrees extremely well with these data, as seen in Fig. 26. 89 Comparing Figs. 25 and 26, the Zr(n,2n) cross section at 14 MeV is seen to 90 89 be about 33% higher than that for Zr. This results partially because the Zr (n,2n) threshold is about 2.5 MeV lower. For energies around 18-20 MeV, increased 89 90 charged-particle emission reduces the Zr(n,2n) cross section relative to Zr. It should also be noted that according to our calculations, approximately 89 90% of the Zr(n,2n) cross section for incident 14-15 MeV neutrons results from 88 population of discrete final levels in the residual Zr nucleus. This situation again indicates the necessity for accurate level scheme information and, because level-density effects are reduced, provides stringent tests on the neutron transmission coefficients used. 88 The calculated Zr(n,2n) cross section is compared in Fig. 27 to the one 38 available data point around 15 MeV. The curve lies around 15% higher than the experimental value, leading to an underprediction in the charged-particle emis- 88 sion cross section calculated for Zr. Considering, however, the difficulties

33 -| i r TT 1.4

1.2

1.0

LU 0.8 00 en 2rr 0.6- 90Zr(n,2n)89Zr o 0.4-

0.2

! . 1 i I I I I 1 l_ J 12 13 14 15 16 17 18 19 20 NEUTRON ENERGY (MeV)

Fig. 24. 9Q 8g Calculated and experimental data for the Zr(n,2n) Zr reaction Ref. 33, O Ref. 40, X Ref. 60, A Ref. 61, D Ref. 62, and • Ref. 63).

0.30

0.25 -

0.20 -

O Ui 0.15 • V) V) O CC O.IO -

O.O5 - Fig. 25. Experimental and calculated yields of the °"zr isomeric state resulting from the 90Zr(n,2n) reaction (A Ref. 34, o 12 14 16 18 20 Ref. 60,A Ref. 61, • Ref. 65,V Ref. 66, NEUTRON ENERGY (MeV) • Ref. 67, O Ref. 68, and # Ref. 71). 34 12 1 1 1 1 1 ^^_

89Zr(n ,2n)88Zr 1.0 — r 08 - / z o 06 - -

SECT I /

04 - CROS S / 02 / -

/ 1 1 10 12 14 16 18 20 NEUTRON ENERGY(MeV)

Fig. 26. Calculated and experimental (Ref. 72) values for the89 Zr(n,2n)88Zr reaction.

1 1 1 1 88 87 Zr(n,2n) Zr ^ ^

0.6 — JQ L / z o / 0.4 - SECT I en /

CRO J 0.2 - /

•/, , 1 12 14 16 18 20 NEUTRON ENERGY(MeV)

Fig. 27. The present calculations are compared to the data of Ref. 38 for the 88 reaction. 35 Involved In both the experiment and calculation, this agreement is still reasonable. 3. (n,p) and Proton-Production Cross Sections. While no total proton- 90 89 production data exist for Zr as was the case for Y, there are data concern- 90 ing the Zr(n,p) reaction and one experimental measurement of the cross section 88 resulting from Zr(n,np + n,pn + n,d) reactions. 90 In Fig. 28 we compare our calculation to the Zr(n,p) experimental results. 40 Our curve lies lower than the excitation function data of Prestwood (1961, 73 closed triangles) and the 1966 data of Carroll. However, at 14-15 MeV, the 74 75 64 more recent measurements of Tikku, Levkovsky, and Qaim (open triangle, closed circle, and open circle, respectively) agree better with our calculated value of approximately 31 millibarns. Also, as shown in Fig. 29, our calculations agree well with the measured values * ' ' for the Zr(n,p) reaction leading to the (E = 0.682 MeV, j" = 7+) isomeric state in 9°Y. QQ X JJQ oy For the Zr nucleus, there exist data for the production of Y through QQ the Zr(n,np + n,pn + n,d) reactions. Information is also available for the production of the isomeric state in Y (E = 0.381 MeV, j" = 9/2+). Our calcu- X lations are compared to these data in Fig. 30. As noted in Sec. III. C. 2, our o o calculation overpredicts the Zr(n,2n) cross section; this in turn leads to the slight underprediction shown in the figure. D. Cross Section Trends for Zirconium Isotopes In this section, as we did in Sec. III. B for yttrium, we compare calculated or evaluated cross sections for the zirconium isotopes studied here. By doing so, one Can obtain an overall view of cross-section magnitudes and their behavior as a function of isotope and incident-neutron energy. 88—90 Figure 31 illustrates the behavior of capture cross sections for the Zr 90 isotopes. For Zr, below 0.1 MeV we have included the average cross-section results of Boldeman since resonance effects are important here. These were joined to Hauser-Feshbach calculations for energies greater than 0.1 MeV. To our 90 knowledge no experimental data exist for the Zr(n,Y) reaction above several hundred kilovolts, and therefore one has to rely on calculational results. For all three isotopes, the effect of the El gianfc-dipole resonance is evident in the 88 89 region between 10-20 MeV. With Zr and Zr, a large compound nucleus contribution results in a distortion of the resonance shape. As was the case for the yttrium calculations, all 2irconium capture cross sections were calculated with 36 - ' ' •• T - 1 r- i i i -• i 1 1 T i i

• ^

90Zr(n ,P)9°Y g 0.01 cj / i, l i LU CO / co to o - ca i-Q- i

o 1

1 i 1 j i i—i 0001 7 20 6 10 12 14 16 18 NEUTRON ENERGY (MeV)

Fig. 28. Calculated and experimental 902r(n)p) cross-section values (A Ref. 40, O Ref. 64, D Ref. 73, A Ref. 74, and • Ref. 75).

ooi -

z o

en oCO

0001 10 12 14 16 18 20 NEUTRON ENERGY (MeV)

Fig. 29. 90., Calculated and experimental yields for the '"Y isomeric state resulting from the ^^Zr(n,p) reaction (A Ref. 68, • Ref. 69, D Ref. 71, and O Ref. 75).

37 0.6 1 I I T 88Zr(n,np + npn) 87Y 0.5

METASTABLE 0.4

O 0.3 LJ to CO

O n, a: 0.2

0.1

1 1 10 12 14 16 18 20 NEUTRON ENERGY ( MeV ) Fig. 30. The calculated yields for 8'Y and 87mY from the 88Zr(n,np + n,pn + n,d) reactions are compared to the data of Ref. 38.

0.001 0.01 0.1 1.0 10.0 NEUTRON ENERGY (MeV)

Fig. 31 88_9Q . Trends in calculated capture cross sections for Zr. The 90zr(n)y) cross section below 100 keV is based on the average capture data of Boldeman.-'-'' 38 90-92 89 the El strength function determined from a fit to Zr(n,y) data. The Zr(n,y) reaction has the highest cross section because its neutron-binding energy of 11.98 MeV is the greatest of the three isotopes, providing the largest integration range for calculation of this cross section. 88—90 89 In Fig. 32H Zr(n,2n) cross-section trends are displayed. The Zr and 90 Zr(n,2n) reactions have thresholds that differ by approximately 2 MeV, but at higher energies the difference in cross sections is less than 10%. On the other 88 hand, for Zr this cross section is quite different, being smaller by almost a factor of two. Here the (n,p) and (n,pn) cross sections are calculated to be quite large, which in turn lowers the fraction of the total reaction cross section available for the (n,2n) reaction. Competition from the (n,np) reaction also plays a role in lowering this cross section in comparison to those values com- . . 89, . 90, puted for Zr and Zr. 88—90 Cross-section characteristics for Zr(n,p) reactions are shown in Fig. 88 89 33. The unstable ' Zr isotopes have positive Q values for this reaction. The 89 fact that the Zr(n,p) reaction has the largest positive value (3.6 MeV) leads QQ to a substantial contribution at low energies. The Zr(n,p) Q value is less (1.46 MeV), leading to reduced cross sections for energies less than a few hundred keV. However, this situation changes above 1 MeV, where substantial cross- section values are predicted. 88—90 The Zr(n,np) + (n,pn) reactions are shown in Fig. 34. The shape of the 90 89 curve shown for Zr is somewhat different than that in Fig. 20 for Y since no 90 bump occurs. This results because in the Zr compound system, the proton neutron 89 binding-energy difference is less than for Y. Also, the proton binding energy 90 in Zr is about 1.3 MeV higher. In this case note that the thresholds for the (n np) + (n,pn) reactions are about the same (7-8 MeV) for all three isotopes. 88 89 Q0 However, the calculated curves for ' Zr lie above that for Zr largely as a result of 30-40% contributions from the (n,pn) reaction.

IV. SUMMARY We have described an extensive series of calculations of neutron-induced reactions on yttrium and zirconium isotopes performed using consistent sets of input parameters and calculational techniques. Calculations made in this mass region around the closed neutron shell lead to the ability to test model parameters in somewhat unusual circumstances not always occuring in other regions. These parameters were determined with a variety of techniques from the use of

39 I 2

88-9OZr(n,2n) 10

0.8

CO CO O g0.4

02-

I L 8 10 12 14 16 18 20 0 001 O.OI 01 1.0 100 NEUTRON ENERGY(MeV) NEUTRON ENERGY (MeV)

Fig. 32. Fig. 33. The calculated (n.2n) cross sections Calculated °°~"^Zr(n,p) cross sections are compared for °^^° in the energy range from 0.001 to 20 MeV.

o UJ m tn tn O cc o 0 01 -

0.001 10 12 14 16 18 NEUTRON ENERGY (MeV)

Fig. 34. The sum of (n,np + n,pn) cross sections as calculated for the 8o-90zr isotopes.

40 independent neutron data such as total cross-section results to the use of information from charged-particle reactions. The calculated results were tested rigor- go QQ ously against a,large portion of the available experimental data for Y and Zr isotopes. This comparison was extended to data for unstable isotopes of these nuclei with satisfactory results. The degree of effort involved in these parameter determinations as well as the fact that most calculated results agree well with experimental data, leads to increased confidence in the ability of these calculations to provide reasonable cross-section results in nearby mass and energy regions lacking in experimental data.

APPENDIX A

DISCRETE LEVELS USED IN THE PRESENT CALCULATIONS

Nucleus Level Energy (MeV) Spin Parity

0. 1.0 0. 000000 5.0

2.5 * • 005000 1.5 4.5 • 390000 1.5 7.5

0. 000000 2.0 3.3 6.3 f

2.5 1.5

,8700130 sis • •i t 37U86 2.0 • 2.0 ,555900 6.0 ,557000 ,780000 s[ a .87J000 5,0 .979000 m 37^*7 • ,386000 is ,873000 1.5 m 41 Nucleus Level Energy (MeV) Spin Parity

3.3 • 1.0 - 1.0 • * 7 »•*<•••>

2.5 •

.7930ii0 2.13

n.4 4 0 .0 4 3 .3 •

«,.5 4 3,.5 4 .5 at 1,.5 » 2,.5 4 1,,5 4 .937000 2..5 - 1.155^^0 1..5 1.22MP0P 3.,5 4 «.,5 • 1.,5 •• 1. 2. 5 4 1. 2. 5 4 1. 2. 5 4

3,000000 n. H • 1.076650 2. 0 + 2. 0 4 0 • 2,229700 a •• 3'. m 6, 0 4 5, 0 * 2. 4 6. 0 + 2.87R000 a. 0 4 8. 0 4 3. 0 . 4. 0 m 3. 3. 0 m

42 Nucleus Level Energy (MeV) Spin Parity 3B087 ^.flPl^fllAF 4.5 • . 5 - 1.5 - 2.5 • 2.5 + 2.5 • S.5 • 2. 2.1 2.237P'iv»i

.•1. A • 2. a • ?.7

2.5 • .5 •

I.93jPi«t» 3[5 t 1.5 • «.5 • 5.5 - .5 - 1.5 + 1.5 - 5.5 • 3.5 •

2..) + 2./1 f 2.H • 3.3 + 2.571P0P 1((f, t 4 . »ii •

1. 3. {"39^0(1 1

43 Nucleus Level Energy (MeV) Spin Parity a,000000 2.5 ,093600 1.5 ,U39000 1.5 * 1,042000 2.5 1,231000 .5

fl.000000 0.0 .815F0P 2.0 1.385000 2.0 1,778000 2.0 2.0*8000 2.3 2,l«1030 4.0 • 2.5?7000 5.0 2.0 P.7P30-3P J. a ?,821000 1.0

0,000000 .5 • ,y2tf0d0 a.5 .2680^0 2.5 • , m 703c 1.5 ,«3b030 1.5 ,639000 1.5 • ,805000 1.5 • ,883000 2.5 • ,936030 .5 m ,96?00F 1.5 m 1.212P00 1.5 m 1,278030 2.5 • 1.37^000 .5 •f 3^86 0.H000U0 4.0 » ,208000 5.0 • .218230 8.0 ,243000 2.0 • ,271030 1.0

0,^00000 .5 * ,381000 0.5 ,792030 2.5 * ,98fe030 1.5 • 1,15^000 2.5 1,180000 1.5 • 1,605000 «'.5 1,848030 1.5 • 2.tf000fl0 3.5 2.^85000 1.5 • 2,150000 2.5 2.2&303F a.5 2,278030 2.5 • ?, 407000 2'. 5 ?.510030 4,5 2,730030 2 5 • Nucleus Level Energy (MeV) Spin Parity

a..? - b. A «•

8. a • .7^7000 2./ - .71S 7.J •

.«13 nfci PI

S.» - 2.^ • 3.

a.yi - 1 . 390B9 .5 -

2, 2.5 • 3.5 t 5.5 • 'J.5 • 2.87J00F 3.5 • 1.5 - 1.5 - 3. 3.1 SBPirfPi .5 • 3.5 • 3. S.b * 5. 3.5 • 3.51 1.5 - .5 - 'J.5 • 2.5 • 3. «.5 + 2.5 • 2.5 - 1.5 - .5 • Nucleus Level Energy (MeV) Spin Parity

2.a 3,0 • 7.0 .77/000 2. * 3.4 l.l 5.0 1. 4.0 1 .215000 0.3 * 1. 6.3 • 1 r.i.a • 1 .41 7000 3'.0 1.S7VHPI00 1.6M0.10 1.0 1.76000P1 J.0 l.fli3PW 3. a .b .5 1.5 2 '.5 1. 3 .5 • to 2 .5 • 1. 1.5 m 1. 3 .5 m 1. 3 .5 + 1. 2 .5 ?. 2 .5 2. 1 .5 • 2. 2:.5 •

0.1 ?;.0 • .280000 3,.0 1* 4,.0 m 1 <. *> m 2,.4 m 1,,3 m 1 3.,* m 1 0.,0 • 1 1.,0 I.U80000 2.,0 1.711000 3.,21 + A. •,5 1. S • 4. 5 2. 5 * 1.130000 2. 5 m 1.29^000 2. 5 m 1.540000 1, 5 m 1,700000 2. 5 • 1.87fc)000 2. 5 • 2,000000 1. 5 m 2,070000 5. b m 46 Nucleus Level Energy (MeV) Spin Parity 40087 «.b + 3.b .5 i.b 5.b 3.b I „ n n 7 s 2.b 1 a.5 + 40088

2.21 •

?,2?bP 8./

.5 - l.b • ?.5 - «.b +

t.5 - 2.5 • l.b - 1,9«3M00 h.S + ?,0«7l*0(?J I.S • 2,lwtf!?^P) 2.5 - b.b • b.b -

47 Nucleus Level Energy (MeV) Spin Parity

& . A *• ft # A • a. A •*• 2.31

Um'A • 3. 4 n 9 CM f ?./i + 3 , 4 '•« & P 3 0 b./ +

1.1

I . c? R .3 f /. M

UtA •

i .i?W5«3t1 .5 +

p.rtflHiJfl 1.5 •

APPENDIX B DETERMINATION OF LOW ENERGY CROSS SECTIONS FOR REACTIONS WITH POSITIVE Q VALUES

In cases involving positive Q-value reactions, we have provided cross sections down to the lower energy limit used in ENDF/B of 10 eV. For the stable 89 90 Y and Zr nuclei resonance parameter and thermal cross-section, information exist that allowed us to determine cross sections in energy regions where Hauser- Feshbach techniques are no longer applicable. For the other nuclei, estimates had to be made of the energy at which resonance effects should become important. Since we used gamma-ray strength functions (Sec. II. C) to normalize our gamma-ray trasnmission coefficients, it was possible to obtain a calculated value of the ratio 2ir/. When assumptions concerning the value of the average gamma-ray width were made, then the average s-wave resonance spacing 48 could be deduced. This in turn provided an estimate of the position of the first resonance occurring in a particular compound system. For yttrium and zirconium isotopes we chose values for of 0.1 and 0.15 eV, respectively. Substituting this in the calculated 27r/ ratio resulted in the values shown in Table B-I. We then used these values to place the 89 location of the first resonance and assumed a shape similar to that of the Y(n,Y) 45 reaction at low energies. (We did not assume the interference dip appearing before the resonance peak in this data.) For the unstable isotopes this resonance peak cross section was joined smoothly to the Hauser-Feshbach results at energies 90 91 around 1 keV. In some cases ( ' Y), experimental thermal cross-section values were available that were then extrapolated using a 1/v dependence and then joined to the lower energy side of the resonance shape. In the other cases a similar procedure was followed, but estimates for thermal cross sections were made on the basis of systematics in this mass region.

TABLE B-I

RESONANCE SPACINGS DEDUCED FROM CALCULATED 2TT/ RATIOS

Target Nucleus (eV) (Deduced) 86 y 5.0 75.0 88 Y 30.0 90 y 353.0 91y 742.0 88 67.0 L 349.0 89Zr 27.0

49 o APPENDIX C ENDF/B REPRESENTATION OF THE YTTRIUM AND ZIRCONIUM CROSS SECTIONS CALCULATED OR EVALUATED IN THE PRESENT WORK

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75 A FEW MISCELLANEOUS RF^ARKS ABOUT THE PRESENT EVALUATION, la51 39 ALL CROSS SECTIONS LEADING To UNSTABLE RESIOUAL NUCLEI OK META» STABLE STATES WERE CALCULATED FO9 ALL RFACTIONS. (MFTASTARLF 399? STATES HERE NOT GENERALLY CALCULATED FOR (N,GAMMA) AND (N,ALPHA) REACTIONS), THE CONVENTION USED IS IF TH FINAL STATE FLAT, (LFS) US1 E 1«51 IS E3UAL TO ZERO THF.N THE CROSS SECTION GIVEN REPRESENTS THE 3990 last aa CROSS SECTION FOR THAT REACTION. CRO SECTIONS LEADING TO SS laSl Q5 STATE ABE OFVOTEO BY LFS FQUAL TO THE NUMBER OF 3990 <*b STATE, FINALLY THF fN,AL»HA) AND fN,ALPHA,N) CROSS SECTIONS ARE 3990 a7 1 '151 499tf REFERENCES last 3990 1/451 4990 p last 1. C.H.JOHNSON ET *L. NjCL. HYs. M* 7, 2U 1 9*8). AND luSt S2 PHYS, REV, LETT. 39,1M4(1977) I'aSt 2, CH, LAGRANGFf NATIONAL SOVTFT CONFERENCE DM PHYSICS 399i? last (1975) 1 '451 3. D.G, 5ARDMER AND M. A, GARDNE 9, «AP«52 17 last hi 9 1 .'4 S1 by. 11 1 aSt hS 17 last

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~~-CtUS. Government Printing Office: 1979 - 677-013/74~~