s- and p-wave neutron spectroscopy Xf(i). Intermediate structure in the 28Si + n reaction: R-matrix interpretation of experimental data

A multilevel R-matrix analysis of Si neutron cross-section data measured at NBS has been performed up to about 4.5 MeV neutron energy. Only a small fraction of the p- and s-wave s.p. strength is observed, but both exhibit local concentrations of strength indicative of doorway structure around 1 and 0.2 MeV, respectively. Besides the well-known 180 keV, strong, $\text{1}\text{2}{}^{\mathrm{+}}$ resonance, the s-wave resonance structure is of moderate strength and widely distributed. The f- and d-wave assignments are not unambiguous, but J > 3/2 resonances show strong signs of intermediate structure for d-waves. A possible correlation between neutron and gamma decay channels and the connection between the states observed in (n, n), (d, p), (n, γ), and (γ, n) channels is discussed. A coreparticle doorway interpretation for s and p- waves is presented.     

s- and p-wave neutron spectroscopy Xc. Intermediate structure: 88Sr

Neutron total cross section measurements of natural Sr were made from 50–875 keV using a high resolution proton beam and the ⁷Li(p, n) reaction as a neutron source. These data were analyzed with the help of an R-Matrix code to extract resonance (energies and other) parameters up to about 850 keV. 2p-1h and particle-vibration doorway interpretation of the s-, p- and d-wave resonances is attempted in terms of the sum rule Σγ_n² = γ_d². Predictions based on both of these models agree with the experimental results. As expected the p-wave resonances are stronger than either s- and d-wave structure. Theory accounts for the p-wave strength remarkably well. Possible location of the p-wave s.p. resonance is reproduced with a real potential and its damping due to the imaginary potential is calculated.More fragmentation of the strong p-wave doorways is observed than was expected for a compound nucleus so near ⁹⁰Zr, but a larger strength function is observed apparently due to the p-wave giant resonance.     

s- and p-wave neutron spectroscopy: Part VI. Level density and neutron excess

Neutron total cross-section curves for Ca⁴⁰, Ca⁴⁴, Cr⁵⁰, Cr⁵², Cr⁵⁴, Fe⁵⁴ and natural Fe, Ti, and Cr have been measured in the kev region. Level spacings have been estimated for the predominant isotope in each of the samples measured, and are compared to similar data found for even N, odd Z targets. After correcting for differences in the angular momenta and excitation energies, it is found that on the average (between A = 35 and 60) $\text{d [}\text{ln}\text{D}{}_0\text{(6}\text{Mev}\text{)] = (?}\text{ln}\text{D}{}_0\text{?Z}\text{)dZ + (?}\text{ln}\text{D}{}_0\text{?N}\text{) dN ? 0.3 dZ ? 0.3 dN}$, and hence D₀(6 Mev) is proportional to exp ?0.3(N ? Z). D₀(6 Mev) is the spin and energy independent spacing parameter. Except for slight signs of a maximum at N = 28, D₀ (6 Mev) appears (between A = 35 and 60) to be strongly dependent only on the neutron excess, N ? Z, and not on N, Z, or A; uncertainties in the correction for excitation are such that it is likely that the absolute value of the exponent, 0.3 (N ? Z) is a lower limit. Isotopic and J^π assignments of many resonances in the natural fluorine and chromium cross-section curves are suggested.     

s- and p-wave neutron spectroscopy: Part VII. Widths of Neutron Resonances

Neutron reduced widths Γ_n⁰ and Γ_n¹ are reported for about 200 resonances observed in neutron total cross sections of Ca^{40, 44}, Ti⁴⁸, Cr^{50, 52, 54}, Fe^{54, 56}, Ni^{58, 60}, Sr⁸⁸, Y⁸⁹, Sn¹²⁴, Te¹³⁰, Ba^{136, 138}, and Pb^{206, 207, 208}, in the energy region 1 to 200 ^kev. Average parameters $\text{Γ}{}_{\mathrm{n}}{}^0$, $\text{Γ}{}_{\mathrm{n}}{}^0\text{D}$, and $\text{Γ}{}_{\mathrm{n}}{}^{\mathrm{(1)}}\text{D}$ have been derived and the Wigner distribution for local spacings and the Porter-Thomas distribution for reduced widths are verified for the resonances in the even-even nuclei Ca⁴⁰, Fe⁵⁶, Ni⁵⁸, and Ni⁶⁰. A simple method of area analysis which is less tedious and time consuming than the method reported before in Part III is also described.     

s- and p-wave neutron spectroscopy: Part V. Level Spacings in Heavy Nuclei

Total neutron cross sections were measured for natural rubidium and thallium and for the separated isotopes, Pb²⁰⁸, Pb²⁰⁷, Pb²⁰⁶, Tl²⁰³, and Rb⁸⁵. Approximate s-wave resonance spacings were estimated for Pb²⁰⁷, Y⁸⁹, Rb⁸⁷, Rb⁸⁵, Tl²⁰³, and Tl²⁰⁵. D₀ = D_J(2J + 1) = 2D_S(2I + 1) = 50, 24, 8, 4, and 30 kev, respectively, where D_s is the average (s-wave) level spacing for all channels. The spacings (D₀) of Pb²⁰⁶ and Pb²⁰⁸ were found to be of the order of hundreds of kew; there is also evidence that resonance spacings are very wide for Sr⁸⁶ and Ba¹³⁶. It is concluded that, in all compound nuclei with a neutron number silightly less than the magic numbers 50, 82, and 126, the resonance spacings are usually not much less than when the magic number is exceeded slightly. Since neutron excitation energies of these sub-magic nuclei are higher than the average, the observed wide level spacings below the magic numbers must be due to the properties of the nearly closed shells and can not possibly be caused only by low excitation energy of the compound nucleus. In considering these comparisons it is shown that, for s-wave resonances, the relation $\text{D}{}_{\mathrm{J}}\text{=}\text{D}{}_0\text{(2J + 1)}$ is a useful approximation in that a plot of D₀ is a much less erratic function of A than is the observed spacing. We also discuss the Bethe-Hurwitz effect, i.e., the influence on resonance spacing (apart from the 2J + 1 factor) of an unpaired nucleon in the target nucleus. We estimate that $\text{α ≧ 30}$ in the equation $\text{D}{}_0\text{(0)}\text{D}{}_0\text{(W)}\text{=}\text{exp}\text{(αW)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ where D₀(0) is the energy and spin independent spacing parameter, and W is the excitation energy of the compound nucleus.     

Fission time in the 28Si + natPt reaction

The experimental fission times are analyzed for excited nuclei produced in the ²⁸Si + ^natPt reaction. Experimental lifetimes obtained by the crystal-blocking technique range between 10^?17 and 10^?18 s at bombarding energies between 140 and 170 MeV, respectively. Experimental data are analyzed within the statistical theory of nuclear reactions and the double-humped-fission-barrier model with allowance for preequilibrium processes and the nuclear-dissipation phenomenon. It is shown that fission barriers retain their double-humped structure for nuclear temperatures up to about 1.7–1.8 MeV and that the lifetimes of excited strongly deformed states in the second potential well contribute substantially to the observed delay times in the fission decay channel.     

Deformation effects in the 28Si+12C and 28Si+28Si reactions

The possible occurrence of highly deformed configurations is investigated in the ⁴⁰Ca and ⁵⁶Ni di-nuclear systems as formed in the ²⁸Si + ¹²C, ²⁸Si reactions by using the properties of emitted light charged particles. Inclusive as well as exclusive data of the heavy fragments and their associated light charged particles have been collected by using the ICARE charged particle multidetector array. The data are analysed by Monte Carlo CASCADE statistical-model calculations using a consistent set of parameters with spin-dependent level densities. Significant deformation effects at high spin are observed as well as an unexpected large ⁸Be cluster emission of a binary nature.     

25Mg (α, n)28Si and 26Mg(α, n)29Si as neutron sources in explosive neon burning

The yields of neutrons from the reaction ²⁵Mg(α, n)²⁸Si and of γ-rays from the reaction ²⁵Mg(α, nγ)²⁸Si have been measured as a function of bombarding energy over the range 1.8–6.3 MeV, and the yield of neutrons from ²⁶Mg(α, n)²⁹Si has been measured over the range 1.8–6.0 MeV. Cross sections for ^{25, 26}Mg(α, n)^{28, 29}Si were extracted from the data and compared with global statistical-model calculations. The agreement is very good. Thermonuclear reaction rates under stellar conditions appropriate for explosive neon burning are calculated and their significance for the nucleosynthesis of rare neutron-rich nuclei is discussed.     

Nuclear structure and direct reaction mechanism in neutron scattering on 28Si in the energy range 6.8 to 14.8 MeV

The structure of excited states in ²⁸Si as well as the energy dependence of the reaction mechanism are investigated. Angular distributions related to the 0₁⁺, 2₁⁺, 4₁⁺, 0₂⁺, 3₁⁺, 2₂⁺ + 2₃⁺, 3₁⁻ + 4₂⁺ levels in the ²⁸Si(n, n′) reaction were measured at incident energies 6.8, 7.0, 8.0 … 12.0 MeV. The analysis was extended up to 14.8 MeV bombarding energy. The experimental cross sections are described by means of a coupled-channel calculation including compound nucleus contributions. The low-lying excited states can be interpreted by a rotational model with prolate but also with oblate g.s. deformation. For the higher-lying states various coupling schemes have been tested. Especially, a second rotational band could be described adopting an oblate deformation.     

The oblate state in 28Si: Alpha cluster structure and point symmetry

The discrepancy between Hartree-Fock and alpha-cluster model results for the oblate minimum in ²⁸Si has been resolved by releasing the point symmetry restrictions that are customarily imposed on the variational space of alpha cluster model calculations.     

Alpha-particle production in the reaction 6Li+28Si at near-barrier energies

The production of alpha particles in the 6Li+28Si reaction was studied at near-barrier energies. Angular distributions were performed at four bombarding energies, namely, 7.5, 9, 11, and 13 MeV. The distributions were characterized by a Gaussian shape, which was integrated in order to obtain alpha-particle cross sections. Our results were compared with previous data of 6Li scattering on various heavier targets and found to exhibit a universal behavior. Present continuum-discretized-coupled-channel calculations support the obtained data. The consequences of the systematic behavior of the alpha-particle production on the unusual behavior of the imaginary potential observed previously in elastic scattering of weakly bound systems is discussed.     

Measurement of the ground state 2n pickup probability for 28Si+68Zn and its role in sub-barrier fusion enhancement

The ground state and excited state transfer yields for the 2-neutron pickup channel in the ²⁸Si+⁶⁸Zn system have been measured explicitly. The recoil mass separator at the nuclear Science Centre, New Delhi was used for the measurement. A NaI(T1) detector was used for detecting the deexcitation γ’s from the transfer products. The kinematic coincidence technique was employed for the transfer measurement. Simplified coupled channels calculations show that out of all transfer channels the major contribution to the sub-barrier enhancement comes from the ground state 2 neutron pickup channel with a ground state Q-value of+1.83 MeV.     

The reaction 26Mg(3He,n)28Si at 23 and 45 MeV

Angular distributions of neutron groups from the ²⁶Mg(³He, n)²⁸Si reaction have been measured at bombarding energies of 23.1 and 45.5 MeV. The experimental results are compared with DWBA and coupled-channel calculations. The zero-range DWBA calculation using shell-model two-nucleon spectroscopic amplitudes explains rather well most of the experimental data of the lowest four states in ²⁸Si, but it is necessary to take two-step processes into account to reproduce all of them satisfactorily. A strong neutron group observed at about 6.9 MeV in residual excitation is described as one composed of unresolved four groups, of which three are attributed to positive-parity states in ²⁸Si predicted in this energy region by the shell-model calculation and one to the 6.88 MeV 3⁻ state in ²⁸Si.     

High resolution gamma-ray spectroscopy of the27Al(p,γ)28Si resonance reaction

High resolution gamma-ray spectra have been measured from the²⁷Al (p,γ)²⁸Si reaction for the resonances atE _p=2·482, 2·511 and 2·735 MeV at ϑ _pγ=0°, 30°, 55° and 90° using a Ge (Li) gamma spectrometer. From the spectra and the angular distributions the properties of the resonance states have been obtained. These states are the isobaric analogues of the levels at 4·69, 4·75 and 4·93MeV levels respectively in the parent nucleus A²⁸l.     

New source of decoupling of E1 strength from the GDR: boundary condition mixing for s- and p-wave neutron states near threshold

Non-statistical effects in neutron capture reveal that E1 strength of neutron orbits of low l-value is partially decoupled from the GDR. Particle-hole diagonalisations with realistic forces do not show this effect. We show that it can arise from a new source, boundary condition mixing, which operates when fine-structure states are introduced. This may also explain the ‘pygmy dip’ in E1 strength reported for masses ～ 195.     

S- and P-wave neutron spectroscopy Part Xd: Intermediate structure, particle-vibration states

The weak coupling particle-vibration model is extended to lowlying neutron resonances in certain even-even or odd-odd nuclei by coupling the extra particle to core excited states of the odd mass target. The odd hole or particle in the target is treated as a passive spectator. ²⁰⁸Pb and ²¹⁰Bi are studied as test cases and the calculated resonance quantities are in good general agreement with the average features of high resolution experiments. The resonances in ²⁰⁸Pb and ²¹⁰Bi are related to the same intrinsic doorway in ²⁰⁹Pb. The ²¹⁰Bi data is presented here for the first time.     

Gamma-ray multiplicity measurements in the28Si+64Ni reaction at 163.8 MeV

The²⁸Si+⁶⁴Ni reaction at 163.8 MeV incident energy is studied by measuring in coincidenceγ-rays and charged particles identified from Z=2 to Z=16. The transition from quasi-elastic to more damped reactions is observed when the difference between the detected charge and the projectile one is increased. The strong influence of the particle decay on the measuredγ-ray multiplicity is evidenced with the help of the statistical model computer code CASCADE. Dissipative events are well described in the rolling limit with excitation energy equally shared between the fragments. The overall agreement is lost for the fragments with the projectile charge which show a small value of theγ-multiplicity even for dissipative events. This is probably connected with the previously observed non statistical behavior of gamma rays emitted in coincidence with projectile-like fragments. In the alpha-spectrum measured in coincidence with gamma-rays, the deexcitation of fused systems is clearly separated from in flight emission of deep inelastic fragments. The low measured gamma-ray multiplicity for fusion events is qualitatively explained taking into account the effect of alpha-emission in the statistical decay.     

Reaction mechanism leading to angular momentum saturation in the 28Si+12C reaction

Evaporation residues and evaporated light particles were measured for the ²⁸Si+¹²C reaction to separate out the contribution of statistical and non-statistical processes involved in the decay of a hot rotating compound nucleus. Saturation of angular momentum l_cr for a mass-40 system is discussed and compared with the established theoretical predictions to understand the reaction mechanism responsible for it. The role of very asymmetric channels in the dynamical evolution of a fused system is also discussed.     

Local tunneling spectroscopy as a signature of the Fulde-Ferrell-Larkin-Ovchinnikov state in s- and d-wave superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states for two-dimensional s- and d-wave superconductors (s- and d-SCs) are self-consistently studied under an in-plane magnetic field. While the stripe solution of the order parameter is found to have lower free energy in s-SCs, a square lattice solution appears to be energetically more favorable in the case of d-SCs. At certain symmetric sites, we find that the features in the local density of states (LDOS) can be ascribed to two types of bound states. We also show that the LDOS maps for d-SCs exhibit bias-energy-dependent checkerboard patterns. These characteristics can serve as signatures of the FFLO states.