Statistical model calculations for medium and strong absorption in theA=90 region

Calculations of elastic, inelastic and total neutron cross sections as well as of (p, n) reaction cross sections in theA=90 mass region have been performed, using the statistical model of Hofmann, Richert, Tepel and Weidenmüller. The optical model parameters were obtained by Finckh et al. from the neutron decay of IAR in the⁹¹Zr(p, n)⁹¹ Nb reaction. The calculations are in very good agreement with the published experimental data. The optical model parameters proved to be satisfactory up to aboutE _n=8.0 MeV. The present work might be relevant to the evaluation of neutron data for reactor technology.     

Excitation functions for the production of90Nb and88Y by irradiation of zirconium with deuterons

Excitation functions for reactions induced by deuterons on natural zirconium and⁹⁰Zr targets have been measured radiochemically with the stacked foil technique between ≈9 and 27 MeV. The observed reactions are Zr(d,xn)⁹⁰ Nb, Zr(d,axn)⁸⁸Y,⁹⁰Zr(d, 2n)⁹⁰Nb and⁹⁰Zr(d, α)⁸⁸Y. The excitation functions for the reactions⁹¹Zr(d, 3n)⁹⁰Nb and⁹¹Zr(d, αn)⁸⁸Y have been deduced from the results mentioned above. Calculations of the excitation function for the (d, 2n) reaction have been performed with two different treatments, each one taking into account two competitive mechanisms. The compound-statistical model plus Hittmair's stripping theory accounts quite well for the (d, 2n) cross sections observed. However, the agreement obtained with Peaslee-Otozai's theory is excellent and the set of parameters used more reasonable. It has been assumed that the stripping mechanism can have no contribution to the (d, α) reaction. Accordingly, calculations for this reaction have been done using the compound-statistical model and the entire absorption process followed by the evaporation of an α particle. No good agreement is obtained with either theory.     

Mean field for the p+90Zr system in the energy range −60 MeV<E<+65 MeV and single-particle features of proton states in 90Zr from a dispersive optical-model analysis

Data on the scattering of protons with energies 5 MeV<E<65 MeV by ⁹⁰Zr nuclei and data on the energies of proton particle and hole levels in the A+1 and A?1 systems with A=90 are analyzed within the dispersive optical model. The parameters of the mean proton field for ⁹⁰Zr are determined in the energy range ?60 MeV<E<+65 MeV. The predicted single-particle features of the levels (root-mean-square radii of orbits, occupation numbers, spread widths, spectroscopic factors, and spectral functions) comply well with experimental data obtained in (d, ³He), (³He, d), (n, d), and (d, n) reactions for levels near the Fermi surface and in (e, e′p) and (p, 2p) reactions for deep levels.     

The level scheme of91Nb from the reaction90Zr (p, γ)91Nb

The level scheme of⁹¹Nb has been investigated with the reaction⁹⁰Zr(p, γ)⁹¹Nb. Proton energies between 3.0 and 7.2 MeV were used. The γ spectra were taken with Ge(Li) detectors. Primary γ transitions to 36 excited states of⁹¹Nb up to 3.8 MeV excitation energy and many secondary γ transitions from the decay of those states were observed, leading to an extension of the known level scheme. The proton binding energy for⁹¹Nb was determined as (5167± 5) keV. Eleven γ transitions in⁹⁰Zr, part of them new, from the competing reaction⁹⁰Zr(p, p′ γ) were also observed.     

Special features of the isospin splitting of the giant dipole resonance in the <Superscript>90</Superscript>Zr nucleus

Data on the proton and neutron channels of the ⁹⁰Zr photodisintegration were analyzed in detail, basic parameters of the isospin splitting of the giant dipole resonance in ⁹⁰Zr being determined by the properties of these channels. New data concerning the cross sections for the partial photoneutron reactions ⁹⁰Zr(γ, n)⁸⁹Zr and ⁹⁰Zr(γ, 2n)⁸⁸Zr and resulting from a simultaneous correction of data from experiments performed in Livermore (USA) and Saclay (France) by using beams of quasimonoenergetic annihilation photons were invoked. Use was made of information about the positions on the energy scale of states characterized by different isospin values in the ⁹⁰Zr nucleus and nuclei neighboring it, which are members of the respective isospin multiplet. New data on the parameters of the isospin splitting of the giant dipole resonance in the ⁹⁰Zr nucleus were obtained on the basis of a global analysis of data on the giant-dipole-resonance states of the ⁹⁰Zr nucleus, which are manifested in the respective photoneutron and photoproton cross sections and in their decay channels involving states of different isospin in neighboring nuclei.     

Cross section measurements on zirconium isotopes for ~14 MeV neutrons and their theoretical calculations of excitation functions

The cross sections for the ⁹⁴Zr(n,d*)^93m+gY, ⁹⁶Zr(n,γ)⁹⁷Z, ⁹⁶Zr(n,2n)⁹⁵Zr, ⁹⁰Zr(n,α)^87mSr, ⁹⁴Zr(n,α)⁹¹Sr,⁹⁰Zr(n,p)^90mY, ⁹²Zr(n,p)⁹²Y, and ⁹⁴Zr(n,p)⁹⁴Y reactions have been measured in the neutron energy range of 13.5-14.8 MeV by means of the activation technique. The neutrons were produced via the D-T reaction. A high-purity germanium detector with high energy resolution was used to measure the induced γ activities. In combination with the nuclear reaction theoretical models, the excitation curves of the above-mentioned eight nuclear reactions within the incident neutron energy range from the threshold to 20 MeV were obtained by adopting the nuclear theoretical model program system Talys-1.9. The resulting experimental cross sections were analyzed and compared with the experimental data from published studies. Calculations were performed using Talys-1.9 and are in agreement with our experimental results, previous experimental values, as well as results of the theoretical excitation curves at the corresponding energies. The theoretical excitation curves generally match the experimental data well.     

Giant dipole resonances built on excited states in 90Zr through radiative proton capture

We have studied the ⁸⁹Y(p, γ_i)⁹⁰Zr reaction populating the states of ⁹⁰Zr at 0.0, 1.761, 2.186, 2.321 and 2.743 MeV. The 90° cross sections were measured from E_p = 3.7 to 11.5 MeV. The data were analysed by the statistical and direct-semidirect models. Spectroscopic factors of low-lying states in ⁹⁰Zr were determined.     

90,91Zr photoproton spectra and the core-excitation model

Photoproton energy spectra have been measured for the ^90,91Zr(γ,P)^89,90Y reactions at an E_γ endpoint energy of 30 MeV, and for the ^90,91Zr,(e, e'p)^89,90Y reactions at a number of different electron beam energies around E_e = 21 MeV. Isotopically enriched target foils of metallic ⁹⁰Zr(97.65%) and ⁹¹Zr(89.2%) were used, and the proton spectra measured at 90°. Prominent proton groups are observed in the ⁹¹Zr spectra, particularly around E_p ≈ 11 MeV, which closely resemble groups produced in the ⁹⁰Zr photoreactions. Moreover, the correlating non-ground state proton groups are being produced in transitions leaving the corresponding ⁸⁹Y, ⁹⁰Y residual nuclei in excited levels which also correlate in energy. These photoproton groups from ⁹⁰Zr have previously been identified as representing T_> strength. A qualitative explanation is proposed in terms of the core-excitation model, in which the structure in the ⁹¹Zr proton spectrum is described as representing dipole $\text{T}{}_{\mathrm{>}}\text{(T =}\text{13}\text{2}\text{)}$ strength formed by coupling the 2d$\text{5}\text{2}$ neutron to dipole T_> (T = 6) excitations of a ⁹⁰Zr core.     

Improving dosimetric properties of tellurite glasses

Thermoluminscence (TL) properties of quaternary tellurite glass in the form 80(TeO₂)–5(TiO₂)–(15−x)(WO₃)–(x)A_nO_m where A_nO_m=Nb₂O₅, Nd₂O₃, Er₂O₃ and x mol% have been measured. TL main dosimetry peak for each produced glass sample were investigated for ⁶⁰Co gamma rays. Dosimetric properties of the quaternary tellurite glasses have been measured as a function of different compositions of the glass system in different rare earth oxides concentration by using thermoluminescence (TL) detection technique.     

Scattering and transfer reactions for 6, 7Li + 90, 91Zr

Elastic scattering data have been measured for the ⁷Li + ⁹⁰Zr, ⁶Li + ⁹⁰Zr, and ⁶Li + ⁹¹Zr systems at E(Li) = 34 MeV. Inelastic scattering data for the ⁷Li + ⁹⁰Zr and ⁶Li + ⁹⁰Zr systems were also measured for the 2⁺(2.18 MeV) and 3^?(2.75 MeV) states in ⁹⁰Zr and the $\text{1}\text{2}{}^{\mathrm{?}}\text{(0.48}\text{MeV}\text{)}$ state in ⁷Li. Optical model analyses of the elastic scattering data and DWBA analyses for the states in ⁹⁰Zr were performed. The deduced deformation lengths for the 2⁺ state agreed with those extracted in other studies but the deformation length for the 3^? state was smaller. The ⁹⁰Zr(⁷Li, ⁶Li)⁹¹Zr angular distributions were measured for the 1.21 and 2.03 MeV states and the 2.19 MeV doublet in ⁹¹Zr. Also, ⁹⁰Zr(⁷Li, ⁶He)⁹¹Nb angular distributions were measured for the ground states, 0.10, 3.41 and 4.82 MeV states in ⁹¹Nb. The transitions well matched in angular momentum were described by finite-range DWBA calculations, while other transitions displayed the same phase problems seen with heavier ions. The extracted spectroscopic information was consistent with the results of other reaction studies. At the present energy, it was not possible to determine whether the l = 1 phase problem that occurs for heavy-ion single-nucleon transfer reactions on 2s-1d shell nuclei occurs in ⁹¹Zr also.     

Gamow-teller strength distribution in the vicinity of A = 90: (I). Schematic calculation of GT strength in 90, 92, 94Nb

The distributions of Gamow-Teller strength in ^{90, 92, 94}Nb have been calculated utilizing the so-called GT force in the random phase approximation. For ⁹⁰Nb the calculated distribution is in striking agreement with that part of the ⁹⁰Zr(p, n) excitation function leading to 1⁺ excitations in ⁹⁰Nb and qualitative agreement is demonstrated for data from the reactions ^{92, 94}Zr(p, n). Some 25 % of the GT strength is found to lie well below the structureless giant resonance proposed by Ikeda et al. The implications of this result to the β-decay properties of neutron rich nuclei near A = 90 are discussed.     

Core polarization and 5/2+ states in91Nb

The energies and spectroscopic factors ofJ ^π=5/2⁺ states of nucleus⁹¹Nb excited via a reaction transferring a proton to the 2d _5/2 orbit of⁹⁰Zr target state have been calculated. Effective two-body interaction used has been extracted from the experimentally observed two-body energies of (1g ₉ ^2/?1 (n) 2d _5/2(n)), (1g ₉ ^2/?1 (n) 1g _9/2(p)) and (1g _9/2(p)-2d _9/2(n)) multiplets in⁹⁰Zr,⁹⁰Nb and⁹²Nb nuclei respectively. Most of the calculated energies and the strengths ofJ ^π=5/2⁺ levels have reasonably good counterparts in the experimental spectrum, however the calculation shows about 17% strength lying at 6.8 MeV, without having a confirmed counterpart in the observed level scheme. The reduced transition strengthsB(M1) forM l transitions from 5/2^? T>(11/2) state to the various components of 5/2⁺ T<(=9/2) state have also been reported; but the corresponding experimental values are not available. The main feature of the reduced transition strengths is that theM1 transition to the state at 3.69 MeV is inhibited whereas that to the state at 6.79 MeV is enhanced, the relevant core-configuration, interfering destructively in the former case and constructively in the latter.     

Fluctuations in 88Sr(p,p0) and 90Zr(p,p′) in the energy region from 12 MeV TO 13 MeV

The low cross sections in the diffraction minima of elastic proton scattering at 12.5 MeV incident energy and far backward scattering angles for target nuclei with mass numbers A of about 90 were used to investigate compound nucleus effects in the framework of the statistical model. In the case of ⁹⁰Zr(p, p′) energy averaged T^< fluctuations are observed, while in the case of ⁸⁸Sr(p, p₀) resolved structures with a coherence width of Γ = 22 keV are found, which is assumed to be the coherence width Γ^> of overlapping T^> states.     

Improved coupled-channel treatment of the (d,n̄) threshold effect

Calculations for the ⁹⁰Zr(d, p) excitation function in a charge-exchange coupling model suggest that the ($\text{d,}\text{n}$) threshold effect can be explained with the resonant solution of the Lane equations taken as the proton form factor.     

Elektronenlawinen und elektrischer Durchschlag in KBr-Kristallen

^90m Nb was produced by the reaction⁹⁰Zr(d, 2n). Comparison of its half-lives in two different chemical environments (Nb atoms in metallic Zr and in the niobium-fluoride complex) showed no difference greater than the experimental error of 1%, whileCooper et al. have reported that the half-life of^90m Nb nuclei is shorter by 3.6% in metallic Nb than in the niobium-fluoride complex. — In addition, the absolute value of the half-life of^90m Nb in metallic Zr was determined to beT _1/2=(19.2±0.3) sec.     

Spin distribution factors for formation of metastable states of 90Y and 91Y through (n,p) reactions over neutron energies 5–15 MeV

The variations in the isomer ratio with the spin distribution factor were studied to obtain the cross-sections for formation of metastable states of ⁹⁰Y and ⁹¹Y nuclei formed respectively through ⁹⁰Zr(n,p)⁹¹Y^m and ⁹¹Zr(n,p)⁹¹Y^m reactions over the neutron energy range 5 to 15 MeV. The theoretical values of the cross-sections could be obtained very close to the respective literature experimental values by varying the spin distribution factor from 1.5 to 2.75. The limiting value of the cross-section was derived from the maximum value of the isomer ratio at that neutron energy, and for this the spin distribution factor was found to vary from 2 to 3.5 over the neutron energies 5 to 15 MeV. Using enriched zirconium targets, cross-sections for formation of ⁹⁰Y^m and ⁹¹Y^m nuclei at 14.8 MeV neutron energy were also measured in the laboratory; the values obtained are 17 ± 2 mb and 22 ± 2 mb respectively for ⁹⁰Y^m and ⁹¹Y^m. Both these values are close to the corresponding limiting cross-sections at 14 MeV neutron energy.     

Calculated yield of isomer depletion due to NEEC for 93m Mo recoils

In the present work, quantitative calculations were carried out for production and depletion of the ^93m Mo isomer in a relatively simple experiment using ⁹¹Zr beam ions. Such studies could be arranged at existing and operating accelerator facilities, e.g. at GSI or in JINR. The ^93m Mo nuclei produced in a He gas target due to the ⁴He(⁹¹Zr, 2n) reaction will recoil into a gas stopper with a high velocity, being then depleted due to NEEC in highly-ionized species.     

Implications of gauge invariance for pion electroproduction at threshold

We discuss the implications of gauge invariance in the problem of the on-shell extrapolation of the electroproduction low-energy theorems. We show that there is an invariant amplitude which can be evaluated at the Breit threshold either using gauge invariance and on-shell dispersion relations or following the Fubini and Furlan [5] extrapolation method starting from the current-algebra low-energy value of the amplitude. Comparing the two expressions, we find a relation between the electromagnetic pion form factor, F_π (k²), and the axial-vector nucleon form factors, g_A (k²) and h_A (k²).     

Experimental and shell-model studies of the reactions 91Zr(d,p)92Zr and 90Zr(t,p)92Zr

The results of high-resolution studies of the ⁹¹Zr(d, p) reaction at E_d = 12 MeV and the ⁹⁰Zr(t, p) reaction at E_t = 11.85 MeV are presented. Absolute cross sections have been measured for both reactions and (d, p) spectroscopic factors determined. A comparison of these results with earlier data has been made, and although many of the previous assignments have been confirmed, many new features concerning the structure of ⁹²Zr have been discovered. Shell-model calculations have been performed for ⁹¹Zr and ⁹²Zr using a neutron space which includes the $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{1}\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbits and a proton space comprising the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits. Realistic proton-neutron and neutron-neutron interactions based on the Sussex matrix elements were used in the calculations. Spectroscopic factors have been calculated for the ⁹⁰Zr(d, p) and ⁹¹Zr(d, p) reactions and cross sections calculated for the ⁹⁰Zr(t, p) reaction. In general, good agreement between the theoretical and the experimental results has been obtained.