Isospin in halo nuclei: Borromean halo,tango halo,and halo isomers

It is shown that the wave functions for isobaric analog, double isobaric analog, configuration, and double configuration states may simultaneously have components corresponding to nn, np, and pp halos. The difference in the halo structure between the ground and excited states of a nucleus may lead to the formation of halo isomers. A halo structure of both Borromean and tango types can be observed for np configurations. The structure of ground and excited states with various isospins in halo-like nuclei is discussed. The reduced probabilities B(Mλ) and B(Eλ) for gamma transitions in ^6?8Li, ^8?10Be, ^8,10,11B, ^10?14C, ^13?17N, ^15?17,19O, and ¹⁷F nuclei are analyzed. Particular attention is given to the cases where the ground state of a nucleus does not have a halo structure, but where its excited state may have it.     

Excess neutron nucleus <Superscript>11</Superscript>Be as a product of reaction (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">p</Emphasis>)

The (t, p) reaction on the ⁹Be nucleus is analyzed using the mechanisms of dineutron stripping and ⁸Li heavy cluster stripping. It is shown that in the shell model, the wave function of the ¹¹Be(1/2⁺) nucleus formed by adding two neutrons to the 9Be nucleus is constructed from a ¹⁰Be(0⁺) core and a 2s-neutron. This concept of the ¹¹Be(1/2⁺) structure allows us to calculate the reduced width of tritium and a dineutron with a relative orbital angular momentum equal to 1. The differential cross section of the (t, p) reaction is calculated with allowance for the contribution from both mechanisms. The agreement between the theoretical and experimental cross sections of dineutron stripping at narrow angles θ_p confirms the shell model can be used to describe the states of nuclei with complex structure and mixed configurations of different shells.     

Multichannel neutron scattering on <Superscript>11</Superscript>Be nucleus

The effect of the Pauli exclusion principle on the relative motion of colliding light neutron-rich nuclei is investigated within a microscopic method for the examples of the ¹¹Be + n and ¹⁰Be + ² n reactions. The effective interaction of nuclei that is due to the change in the kinetic energy of their relative motion under the effect of the antisymmetrization operator is analyzed on the basis of a discrete representation of harmonic-oscillator states allowed by the Pauli exclusion principle. It is concluded that the bound state of the ¹²Be nucleus owes its origin to the impact of exchange effects on the operator of the kinetic energy of the relative motion of the neutron and the ¹¹Be nucleus. The structure of the ¹²Be ground state is discussed in the approximation of two coupled cluster configurations. The cross section for the inelastic-scattering reaction ¹¹Be(n, ² n)¹⁰Be is estimated.     

Study of the Involvement of <Superscript>8</Superscript>Be and <Superscript>9</Superscript>B Nuclei in the Dissociation of Relativistic <Superscript>10</Superscript>C, <Superscript>10</Superscript>B,and <Superscript>12</Superscript>C Nuclei

The results obtained by estimating the contribution of 8Be and 9B nuclei to the coherent dissociation of ¹⁰C, ¹⁰B, and ¹²C relativistic nuclei in nuclear track emulsions (“white” stars) are presented. The selection of white stars accompanied by 9B leads to a distinct peak appearing in the distribution of the excitation energy of 2α2p ensembles and having a maximum at 4.1 ± 0.3 MeV. A 8Be nucleus manifests itself in the coherent-dissociation reaction ¹⁰B → ²He + H with a probability of (25 ± 5)%, (14 ± 3)% of it being due to 9B decays. The ratio of the branching fractions of the ⁹B + n and ⁹Be + p mirror channels is estimated at 6 ± 1. An analysis of the relativistic dissociation of ¹²C nuclei in a nuclear track emulsion revealed nine 3α events corresponding to the Hoyle state.     

Yields of hydrogen isotopes in stopped-pion absorption by light nuclei

The spectra of p, d, and t charged particles produced in stopped-pion absorption by nuclei are analyzed. Respective measurements were performed for 17 nuclei by means of a semiconductor spectrometer. A phenomenological model developed previously for medium-heavy and heavy nuclei was applied to describing the spectra and yields of charged particles originating from light nuclei (^6,7Li, ⁹Be, ^10,11B, and ¹²C). The contribution of intranuclear clusters (such as pp and ^3,4He) to pion absorption was estimated.     

One-nucleon spectroscopy of light nuclei

The capabilities and limitations of the conventional many-particle shell model and modern potential cluster models are discussed. New revaluated and more accurate calculations of one-nucleon spectroscopic characteristics of the light nuclei of 1p shell are presented. In many-particle shell model for nuclei with A = 7, 9, 11, 13, and 15 nucleon partial widths of highly excited states with the isotopic spin T = 3/2 were calculated both for “allowed” and “forbidden” transitions. One-nucleon spectroscopic factors were calculated in threebody multicluster models of ⁶Li{αnp}, ⁸Li{αtn}, and ⁹Be{ααn} nuclei. For isobar-analogue nuclei ⁷Li and ⁷Be, the spectroscopic proton S _p and neutron S _n factors for transitions to the ground and excited states of corresponding residue nuclei of the triplet ⁶Li-⁶He-⁶Be were calculated in the framework of binary potential αtand ατ models. Integral, differential and polarization characteristics of photonuclear processes ⁷Li(γ, n ₀)⁶Li, ⁶He(p, γ_{0 + 1})⁷Li, ⁷Li(γ, p ₀)⁶He, and ⁹Be(γ, p _{0 + 1})⁸Li were calculated in this approach.     

Structure of β-decay Strength Function <Emphasis Type="Italic">S</Emphasis><Subscript>β</Subscript>(<Emphasis Type="Italic">E</Emphasis>) in Halo Nuclei

It is shown that when the parent nucleus has nn Borromean halo structure, then after Gamow–Teller (GT) β^–-decay of parent state or after M1 γ-decay of Isobar Analogue Resonance (IAR) the states with np tango halo structure or mixed np tango + nn Borromean halo structure can be populated. Resonances in the GT β-decay strength function S_β(E) of halo nuclei, may have np tango halo structure or mixed np tango + nn Borromean halo structure. Correct interpretation of halo structure is important in experiments on β-decay study, interpretation of M1 γ-decay of IAR, and charge-exchange nuclear reactions analysis.     

Investigation of the reaction mechanism for the four-particle photodisintegration of a carbon nucleus

The four-particle photodisintegration of a carbon nucleus in the reactions ¹²C(γ, p)³H2α and ¹²C(γ, n)³H2α is investigated by a method that employs a diffusion chamber in a magnetic field. It is shown that these reactions proceed according a sequential-type scheme: excited states of ¹¹B and ¹¹C nuclei decay to weakly excited states of ⁸Be, ⁷Li, and ⁷Be nuclei. It is concluded that nucleons are knocked out from the s shell. In the excitation curve for the 2α system in the reaction ¹²C(γ, p)³H2α, a resonance is found between the maxima corresponding to the ground and the first excited state of the ⁸Be nucleus, and this resonance is identified as a ghost anomaly. The branching fractions of the decay modes are determined. The angular distributions of nucleons in the reaction c.m. frame are measured. The energy dependence of the asymmetry coefficient for the angular distributions is obtained. A fast increase in this coefficient is observed in the energy range 38–40 MeV. It is concluded that the asymmetry coefficient depends on the excitation energy of the final nucleus in the region of intermediate photon energies.     

Structure of the spatial periphery of the <Superscript>11</Superscript>Li and <Superscript>11</Superscript>Be isobars

On the basis of the shell model with an extended basis, the structure of ⁹Li-⁹Be to ¹¹Li-¹¹Be nuclei is examined with allowance for the competition of ^jj coupling and Majorana exchange forces via considering the sequential addition of neutrons, and the respective wave functions are determined. A formalism for calculating the spectroscopic factor for a dineutron and for individual neutrons in nuclei whose wave functions incorporate the mixing of shell configurations is developed. The reactions ⁹Li(t, p)¹¹Li and ⁹Be(t, p)¹¹Be treated with allowance for the mechanisms of dineutron stripping and a sequential transfer of two neutrons are considered as an indicator of the proposed structure of lithium and berylliumisotopes. The parameters of the optical potentials, the wave functions for the bound states of transferred particles, and the interaction potentials corresponding to them are determined from a comparison of the theoretical angular distribution of protons from the reaction ⁹Be(t, p)¹¹Be with its experimental counterpart. It is shown that a dineutron periphery of size about 6.4 fm is present in the ¹¹Li nucleus and that a single-neutron periphery of size about 8 fm is present in the ¹¹Be nucleus.     

Structure studies of exotic nuclei using (<Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">p</Emphasis>′) reactions

The structure of radioactive beams is investigated using the simplest possible probe: the proton used as a target in inverse kinematic reactions. From (p, p′) reactions, information on the neutron and proton transition densities is obtained through the comparison between the measured inelastic cross sections and the ones calculated using a microscopic potential and theoretical densities. (p, p′) inelastic scattering data to the first excited state for the halo nucleus ⁶He and for other nuclei ³⁴Ar and ^34,36S have been measured at GANIL using the MUST telescopes. This allows one to extract the global features of the transition densities, as shown for the halo nucleus ⁶He. We can also probe the evolution of the shell structure along isotopic chains in moving towards the neutron or proton drip lines. The example of the sulfur isotopic chain is discussed.     

Calculation of the binding energy of heavy nuclei with non-local two-body forces

A non-local, separable potential which matches the phase shifts up to 320 MeV and gives saturation for nuclear matter in the first order at a Fermi-momentum ofk _F =1.6 f^?1 with an energy per particle of ?8 MeV has been constructed byTabakin. We have employed this potential for calculations of finite nuclei using the Fermi-gas-model. The binding energy has been minimalized with respect to two parametersb andc (the surface-thickness and the radius of the nucleus). However the calculations show that an arbitrarily sharp surface is possible.     

Use of (<Superscript>3</Superscript>He, <Emphasis Type="Italic">t</Emphasis>) charge-exchange reactions in determining radii of excited states of nuclei

A method for determining the radii of excited states of nuclei by means of (³He, t) charge-exchange reactions was proposed. Two versions of a comparison of differential cross sections for (³He, t) reactions were considered. The first relies on a comparison with cross sections for inelastic-scattering processes leading to the formation of isobaric analog states, while the second involves (³He, t) reactions leading to the production of the ground state. The two versions in question yield similar results and make it possible to determine the radius of the first excited state of the ¹³N nucleus. This state has the excitation energy of E* = 2.37 MeV, lying above the proton-emission threshold. The resulting radius proved to be enhanced in relation to the ground state and is close to the radius of the 3.09-MeV isobaric analog state of the ¹³С nucleus, which has a neutron halo. This permitted drawing the conclusion that the ¹³N nucleus in the 2.37-MeV state has a proton halo. The possibility of revealing a proton halo in other states of light nuclei is considered.     

Structure of neutron-rich Isotopes <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li and allowance for it in elastic scattering

The differential cross sections for elastic proton scattering on the unstable neutron-rich nuclei ⁸Li and ⁹Li at E = 700 and 60 MeV per nucleon were considered. The ⁸Li nucleus was treated on the basis of the three-body α-t-n model, while the ⁹Li nucleus was considered within the α-t-n and ⁷Li-n-n models. The cross sections in question were calculated within Glauber diffraction theory. A comparison of the results with available experimental data made it possible to draw conclusions on the quality of the wave functions and potential used in the calculations.     

Elastic scattering of intermediate-energy protons on <Superscript>9</Superscript>Be nuclei within the 2<Emphasis Type="Italic">αn</Emphasis> model

The α-cluster model involving dispersion is adapted to the case of the ⁹Be nucleus. Two configurations of the ground state of this nucleus are employed in calculations: (i) a core (⁸Be nucleus) and a complementary cluster (neutron), which oscillates with the highest probability about the center of mass of the core, and (ii) an isosceles triangle formed by two alpha-particle clusters and a neutron. Polarization observables of elastic proton scattering on ⁹Be nuclei are calculated on basis of this approach and the theory of multiple diffractive scattering. The results of these calculations are in good agreement with available experimental data.     

“Alpha decays” of <Stack><Subscript>Λ</Subscript><Superscript>10</Superscript></Stack>Be and <Stack><Subscript>Λ</Subscript><Superscript>10</Superscript></Stack>B hypernuclei: Phenomenological analysis and role of nuclear structure

Hypernuclei are used to study the baryon-baryon weak interaction and associated effective weak Hamiltonian. We will show how the proper choice of hypernucleus can be used to pick out components of the effective weak Hamiltonian. It is well known that removing one nucleon from ⁹Be or ⁹B results in ⁸Be* with a subsequent αα decay. Through this unique process, it would be possible to identify final states of the residual nucleus. So, due to these specific properties of the core nuclei ⁹Be and ⁹B, it may be possible to measure the branching fractions Γ _ααi ^n(p) for the exclusive decays of the _Λ ¹⁰ Be ( _Λ ¹⁰ B) hypernuclei.     

The formation of the superheavy hydrogen isotope <Superscript>6</Superscript>H in the absorption of stopped π<Superscript>−</Superscript>-mesons by nuclei

An experimental search for the superheavy hydrogen isotope ⁶H was conducted through studying the absorption of stopped π^?-mesons by ⁹Be and ¹¹B nuclei. A structure in the missing mass spectrum caused by the resonance states of ⁶H was observed in three reaction channels, namely, ⁹Be(π^?, pd)X, ¹¹B(π^?, d³He)X, and ¹¹B(π^?, p⁴He)X. The parameters of the lowest state E_r=6.6±0.7 MeV and Γ=5.5±2.0 MeV (E_r is the resonance energy with respect to the disintegration into the triton and three neutrons) are evidence that ⁶H is a more weakly bound system than ⁴H and ⁵H. Three excited states of ⁶H were observed. Their resonance levels (E_1r=10.7±0.7 MeV, Γ_1r=4±2 MeV, E_2r=15.3±0.7 MeV, Γ _2r=3±2 MeV, and E_3r=21.3±0.4 MeV, Γ_3r=3.5±1.0 MeV) are energetically capable of disintegrating into six free nucleons.     

Abnormal features of neutron-nucleus low-energy interaction and the mechanism of inhibition of neutron-induced reactions

The features of the distant interaction of thermal and slow neutrons with nuclei are examined. From the Dirac equation analysis it was shown that this interaction is determined by the potential barrier located outside the nucleus. The height of the barrier is proportional to Z ²/A ^4/3 and reaches 110eV for even-even nuclei like U²³⁸ and 25-65eV for even-odd U²³⁵ , U²³³ , Pu²⁴¹ nuclei. This barrier is connected with the non-linear ponderomotive interaction of the neutron abnormal magnetic moment with the strong electric field of a nucleus. The barrier penetrability for thermal neutrons equals 0.9-0.98. For cold neutrons the penetrability decreases greatly and for ultracold ones it becomes very small. At unlimited decrease of the neutron energy, E \( \rightarrow\) 0 , the cross-section of any neutron-nucleus reaction \( \sigma_{{f(tot)}}^{}\) \( \rightarrow\) 0 . So such reactions become impossible. In this work the existence of separated neutron potential wells symmetrically located at r ₀ \( \approx\) (1.3-4.5)×10^-12 cm \( \approx\) (1.7-5)×R from even-odd U²³⁵ , U²³³ , Pu²⁴¹ nuclei is predicted. These wells with depths 0.1-5eV are the result of combined ponderomotive and pure magnetic interactions of the neutron abnormal magnetic moment with nucleus electric and magnetic fields. The presence of distant wells leads to the possibility of the existence of virtual or quasi-stationary neutron-nucleus molecules. Such wells can be virtual traps for thermal and cold neutrons. It was predicted that the neutron halo phenomenon may be connected with such traps.     

Investigation of low-lying levels of the <Stack><Subscript>4</Subscript><Superscript>8</Superscript></Stack>Be nucleus in the multiquantum approximation of the orthogonal scheme

In the multiquantum approximation of the orthogonal scheme, specific calculations for the energies and radii of the ₄ ⁸ Be nucleus are performed with allowance for all states characterized by the λ=[44] Young diagram, the quantum numbers K_min and K_min+2 of the O(3(A?1)) group, and the quantum numbers E=K+2N (N≤9) of the U(3(A?1)) group. The convergence of the results with respect to the extension of the basis is studied, and the structure of relevant wave functions is revealed. The results of these calculations are compared with the results obtained in the analogous approximation of the unitary scheme.     

Role of the nuclear and electromagnetic interactions in the coherent dissociation of the relativistic <Superscript>7</Superscript>Li nucleus into the <Superscript>3</Superscript>H + <Superscript>4</Superscript>He channel

The differential cross section in the transverse momentum Q and a total cross section of (31 ± 4) mb for the coherent dissociation of a 3-A-Ge V/c ⁷Li nucleus through the ³H + ⁴He channel have been measured on emulsion nuclei. The observed Q dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction (Q ≤ 400 Me V/c) and Coulomb (Q ≤ 50 Me V/c) dissociations are calculated to be 40.7 and 4 mb, respectively.