Even-even Target Research Articles

A + 2n compound nuclei and the unitary limit in nuclear physics

This contribution discusses a new perception of the structure of compound nuclei by introducing intermediate states of the Feshbach formalism of nuclear reactions in the Interacting Boson Model of nuclear structure. The stake is to explore the manifestation of the unitary limit in heavy, even-even nuclei. Interactions that govern Feshbach resonances of cold and dilute atomic gases suggest the formulation of an IBM-compound Hamiltonian for scattering two neutrons (2n) from a heavy, even-even target (A). The solutions of the corresponding coupled channel equations host a 2n-IBM state resonance. It turns out that the unitary limit is measurable in a heavy A + 2n compound nucleus at low temperatures. That measurement is feasible through the fluctuations of the cross-sections that tune the 2n-A scattering length.

Microscopic description of target spin distribution after inelastic scattering to the continuum

Microscopic modeling of inelastic scattering to the continuum is applied to neutron induced reaction on spherical and axially deformed even-even targets. The spin distributions of the residual compound nucleus formed after the fast inelastic process are calculated with two microscopic models and compared to the prescription usually associated to the semi-classical exciton model. As the semi-classical exciton model does not account for angular momentum conservation, it is often assumed that it is the same as the compound nucleus spin distribution, but this forgets the dynamics of the reaction. It is found that microscopic approaches drastically reduce the average spin value in comparison to what was previously assumed. This strongly impacts (n,n’ γ) as well as isomer production cross sections when high spin levels are involved. New spin cut-off parameters are deduced from the microscopic calculations that can be used as an alternative to previous prescriptions which neglect the reaction dynamics when they are applied in the context of pre-equilibrium emission process.

Conformal symmetry in nuclear structure

The purpose of this paper is to introduce the unitary limit as applied in systems of cold atoms into collective states of heavy and even-even nuclei and to identify a related physical example. This is accompanied by the determination of observables of conformal symmetry in nuclear structure. A Hamiltonian is defined that governs the scattering process of an incident pair of two slow neutrons onto a heavy, even-even target nucleus in the framework of the Interacting Boson Model of nuclear structure. A unitary pair-collective state interaction is introduced along with the effective range expansion for a pair-collective state scattering length. The solutions to the coupled channels equations provide a scattering state for the two neutrons that couples with an intermediate state of the A+2n compound nucleus. The unitary limit manifests itself when the intermediate states correspond to pair-collective state resonances the positions of which coincide with the energies of IBM states of the closed channels. The position and the width of each resonance is measurable via the fluctuation of the cross section which tunes the pair-collective state scattering length. Conformal symmetry is represented in a tower of equally spaced states that emerges at the unitary limit from two-boson excitations on the IBM state of the closed channel. These tower states are measurable as a regularity pattern of fluctuations of the cross section, in terms of regular positions and widths. The manifestation of the unitary limit and conformal symmetry via fluctuations of the cross section indicates the A+2n compound nucleus as a physical laboratory for the examination of the BCS-BEC crossover, of an underlying critical point and of algebras with infinite number of generators.

Nucleon scattering on actinides using a dispersive optical model with extended couplings

Tamura coupling model has been extended to consider the coupling of additional low-lying rotational bands to the ground state band. Rotational bands are built on vibrational bandheads (even-even targets) or single particle bandheads (odd-$A$ targets) including both axial and non-axial deformations. These additional excitations are introduced as a perturbation to the underlying axially-symmetric rigid rotor structure of the ground state rotational band. Coupling matrix elements of the generalized optical model are derived for extended multi-band transitions in even-even and odd-$A$ nuclei. Isospin symmetric formulation of the optical model is employed. A coupled-channels optical model potential (OMP) containing a dispersive contribution is used to fit simultaneously all available optical experimental databases including neutron strength functions for nucleon scattering on $^{232}$Th, $^{233,235,238}$U and $^{239}$Pu nuclei and quasi-elastic ($p$,$n$) scattering data on $^{232}$Th and $^{238}$U. Lane consistent OMP is derived for all actinides if corresponding multi-band coupling schemes are defined. Calculations using the derived OMP potential reproduce measured total cross-section differences between several actinide pairs within experimental uncertainty for incident neutron energies from 50 keV up to 150MeV. Multi-band coupling is stronger in even-even targets due to the collective nature of the coupling; the impact of extended coupling on predicted compound-nucleus formation cross section reaches 5% below 3 MeV of incident neutron energy. Coupling of ground-state rotational band levels in odd-$A$ nuclei is sufficient for a good description of the compound-nucleus formation cross sections as long as the coupling is saturated (a minimum of 7 coupled levels are typically needed).

Large-scale calculations of supernova neutrino-induced reactions inZ=8–82 target nuclei

Background: In the environment of high neutrino fluxes provided in core-collapse supernovae or neutron star mergers, neutrino-induced reactions with nuclei contribute to the nucleosynthesis processes. A number of terrestrial neutrino detectors are based on inelastic neutrino-nucleus scattering and modeling of the respective cross sections allow predictions of the expected detector reaction rates.Purpose: To provide a self-consistent microscopic description of neutrino-nucleus cross sections involving a large pool of $Z=8$--82 nuclei for the implementation in models of nucleosynthesis and neutrino detector simulations.Methods: Self-consistent theory framework based on relativistic nuclear energy density functional is employed to determine the nuclear structure of the initial state and relevant transitions to excited states induced by neutrinos. The weak neutrino-nucleus interaction is employed in the current-current form and a complete set of transition operators is taken into account.Results: We perform large-scale calculations of charged-current neutrino-nucleus cross sections, including those averaged over supernova neutrino fluxes, for the set of even-even target nuclei from oxygen toward lead ($Z=8$--82), spanning $N=8$--182 (OPb pool). The model calculations include allowed and forbidden transitions up to $J=5$ multipoles.Conclusions: The present analysis shows that the self-consistent calculations result in considerable differences in comparison to previously reported cross sections, and for a large number of target nuclei the cross sections are enhanced. Revision in modeling $r$-process nucleosynthesis based on a self-consistent description of neutrino-induced reactions would allow an updated insight into the origin of elements in the Universe and it would provide the estimate of uncertainties in the calculated element abundance patterns.

Systematical law of (n, γ) reaction cross sections of even-even nuclei

We have derived a formula for the neutron radiative capture cross section in the framework of a statistical model approach to nuclear reactions. Based on this formula, new systematics are established between the (n, γ) reaction cross section and the energy level density of a compound nucleus or a relative neutron excess of an even-even target nucleus for neutron incident energy above the resonance region to MeV. Good agreement with experimental data suggests that this new systematical law is helpful to analyze the experimental data.

Double charge exchange and generalized seniority

The double charge exchange transition matrix elements from an even-even target to the double isobaric analog state and the ground state are derived in the generalized seniority model as a function of the number of valence nucleons. Crucial differences with the seniority model are found and their consequences are discussed.

Effect of configuration admixtures on pion double charge exchange.

A recent two amplitude expression for pion double charge exchange from even-even targets to the double isobaric analog, which is valid for a single shell-model orbital, is generalized to many shell-model orbitals.

Single-particle properties of the 1f2p shell nuclei on the basis of proton stripping and pick-up data

The experimental data on proton stripping and pick-up on even-even targets with Z from 20 to 28 are analyzed jointly using the spin and parity data obtained in different experiments. The general features in the distribution of the spectroscopic strengths among nuclear states are revealed. Spins of 10 nuclear states and parity of one state are predicted. The shell-structure parameters are calculated. It is found that the single-particle forces are essential in the above-noted experiments.

Total Gamow-Teller strengths from measured ground-state correlations

Abstract Recently developed sum rules for Gamow-Teller transitions as observed in (p, n) and (n, p) reactions were applied to all stable even-even target nuclei between 16 O and 58 Ni and to 90 Zr. The total Gamow-Teller strengths S (p, n) and S (n, p), which depend sensitively on ground-state correlations, were calculated by the use of measured occupation numbers deduced from proton- and neutron-pickup and stripping experiments. The results are at variance with experimental observations.

Measurement of the fission cross section of232U for neutron energies in the range 0.06?7.40 MeV

From the physical viewpoint the study of the fission probability of the lightest uranium isotope in the reaction (n, f) gives interesting information about the fissionability of the compound nucleus /sup 232/U, for which the neutron binding energy is apparently close in value to the maximum of the humps in the fission barrier. In this case, the neutron fission cross section of /sup 232/U should not exhibit a threshold, unlike other even-even target nuclei of heavier uranium isotopes (/sup 234/U, /sup 236/U, /sup 238/U). The fission cross section of /sup 232/U was measured relative to sigma/sub f/(/sup 239/Pu), since this nuclide is convenient for measuring the ratio of the numbers of fissioning nuclei in layers by the method of comparing their ..cap alpha.. activity. The experiment was performed on electrostatic accelerators of the FEI. In order to cover the energy range studied, we used the reactions /sup 71/Li (p, n)(E/sub n/ less than or equal to 0.34 MeV), T (p, n) (0.34 less than or equal to E/sub n/ less than or equal to 3.6 MeV) and D (d, n)(E/sub n/ greater than or equal to 3.8 MeV). We used solid targets consisting of lithium fluoride and titanium or scandiummore » hydride on molybdenum substrates. The total energy resolution equalled +- (30-40) keV for E/sub n/ < 1.5 MeV and +- (70-200) keV at higher energies« less

Transfer reaction sum rules and the interacting boson-fermion model

Spectroscopic factor sum rules for single nucleon transfer are studied in the context of the interacting boson-fermion model. These sum rules are applied to pickup and stripping reactions on even-even targets. It is shown that for such targets the odd-even interacting boson-fermion model intermediate states are essentially complete, so that the evaluation of these sum rules using interacting boson-fermion model wave functions and transfer operators is valid. However, this is not true for reactions on odd-even targets. The interacting boson-fermion model sum rules are derived and applied to experimental data from recent studies of the platinum isotopes. A significant discrepancy exists between experiment and theory.

P-wave neutron strength functions in nuclear vibrational region.

The effect of doorway states on the p-wave neutron strength functions is investigated for even-even target nuclei in the vibrational region. A semi-empirical formula including contributions from both doorway state and coupled channel is derived for the p-wave strength function. The calculated results are compared with experimental data. Overall agreement in the mass region of 40~180 is fairly well except for a few nuclides. In addition, isotopie trends of the p- wave neutron strength functions are studied for Cr, Fe, Ni, Zn, Se, Zr, Mo, Ru, Pd, Cd and Nd.

The 159Tb(t, α) 158Gd reaction with 17 MeV polarized tritons

The 159Tb( t , α) 158Gd reaction has been studied using 17 MeV polarized tritons from the Los Alamos Scientific Laboratory Tandem Van de Graaff accelerator. The α -spectra were analyzed with a Q3D magnetic spectrometer. The observed analyzing powers for most of the strong transitions have large magnitudes similar to those observed for ( t , α ) studies with neighbouring even-even targets. This is consistent with a Nilsson model description of the two quasiparticle states populated in 158Gd, in which most of the strong transitions would be expected to be dominated by a single j-value. The present results provide strong confirmation of the previously suggested assignments of the 1380 keV ( K π = 4 +) and 1930 keV ( K π = 1 +) band heads as 5 2 + [413] ± 3 2 +[411] configurations. Several rotational members of the K π = 1 − octupole band were populated via the 5 2 −[532]- 3 2 +[411] component of this vibration, and from the observed strengths it is estimated that this two-quasiparticle admixture makes up ∼45% of the octupole vibration. Strong transitions to several levels above 2 MeV excitation are dominated by l = 5, j = 11 2 transfers, and these are ascribed to pickup of a 5 2 −[532] proton. The spin 5, 6 and 7 members of the K π = 4 −, 5 2 −[532] + 3 2 +[411] band have been assigned at 2176 keV, 2282 keV and 2418 keV, respectively. Whereas previous studies have shown that the (t, α) reaction with polarized tritons is a very useful specroscopic technique when used with even-even target nuclei, the present results extend the proven effectiveness to cases of odd-mass deformed targets.

30 keV (n, ?) cross-sections from the nuclear statistical model

Global input parameters for a Hauser-Feshbach calculation of astrophysical nuclear reaction rates are evaluated; wherever possible they are expressed as systematic functions of nucleon numbersN andZ rather than mass numberA. Average (n, γ) cross-sections at 30 keV are calculated for all stable nuclei and nuclei with lifetimes ≥ 1 yr, taking into account the effects of width fluctuations. Agreement with experimental results is generally obtained to within 70%, but systematic discrepancies arise for even-even target nuclei between neutron shell closuresN=50 andN=82. A σN curve for thes-process nuclei is in good agreement with theoretical predictions, except for a possible anomalous peak aroundA=180.

Compound nucleus (α, p) and (p, p′) reactions on odd-Anuclei in the Ni region

Experimental compound nucleus cross sections are obtained for (p,p') and (..cap alpha..,p) reactions induced by 12 MeV protons and 15 and 18 MeV ..cap alpha.. particles on /sup 55/Mn, /sup 57/Fe, /sup 59/Co, /sup 61/Ni, and /sup 63/Cu. The noncompound nucleus cross sections, estimated from the spectra from /sup 64/Ni, are found to account for at least 20% of the total proton cross sections and also soften the spectra in the (p,p') cases. When these are subtracted off, good agreement in spectral intensities is found between experimental compound nucleus cross sections and predictions using Hauser-Feshbach calculations with Gilbert-Cameron level density parameters. No adjustable parameters were used. The slopes of the proton energy spectra from both (p,p') and (..cap alpha..,p) reactions are consistently flatter (i.e., decrease less rapidly with increasing proton energy) for odd-A than for even-even targets.

Nuclear spectroscopy using (d,αγ) angular correlations

We show that ( d, αγ) particle γ-ray angular correlation measurements are worthwhile for determining the spins of states with J≤4 in residual odd-odd nuclei when the deuterons, incident on an even-even target, are quantized along the beam direction, firstly in their m s = 0 and secondly in their m s = 1 (or −1) substate with α-particles detected at 0° or 180° to the beam direction.

Identification of Jπ = 0 − levels in odd-odd nuclei and the absolute determination of t20 for polarized spin-1 beams

It is shown that J π = 0 − levels in odd-odd nuclei can be anambiguously identified following the ( d , α) reaction on an even-even target; in particular, the 4.91 MeV level in 14N is assigned J π = 0 −. It is also shown that such J π = 0 − levels are useful for the absolute determination of the tensor component ( t 20) of polarized spin-1 beams.

New Technique for Parity Measurement Using Polarized Deuterons

A new model-independent method for determining the parity of a state as either π= (-)J or π= (-)J+1 in odd-odd nuclei is described. The technique requires a polarized deuteron beam to initiate a (d, α) reaction on an even-even target with detection of the reaction products near 0degree or 180degree. The method is demonstrated using the reaction 12C(d, α)10B.

Further studies of pairing excitations in actinide nuclei:U233,Pu237,Np235,Am241,Ra224, andPu238

The behavior of a pairing excitation, previously reported in even actinide nuclei, has been explored with two odd-neutron ($^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$) and two odd-proton ($^{237}\mathrm{Np}$ and $^{243}\mathrm{Am}$) targets as well as the even-even targets $^{226}\mathrm{Ra}$ and $^{240}\mathrm{Pu}$. It is found that this behavior is similar to that previously found in even-even actinide nuclei.[NUCLEAR REACTIONS $^{226}\mathrm{Ra}$, $^{235}\mathrm{U}$, $^{237}\mathrm{Np}$, $^{239}\mathrm{Pu}$, $^{243}\mathrm{Am}$, $^{240}\mathrm{Pu}(p,t)$ measured $\ensuremath{\sigma}(\ensuremath{\theta})$, deduced excitations and cross sections of pairing excited states.]