International Journal of Modern Physics E

A review is given of the relation between pairing, quasi-spin algebras and seniority. The former two concepts are closely connected, the relation being that the quasi-spin formalism allows an efficient solution of the pairing problem. Seniority is of much wider applicability than either pairing or quasi-spin and applications can even be extended to encompass the notion of partial symmetry. A recent application of partial conservation of seniority and its importance for nuclear isomers is discussed.

Structure of symmetrization group and its influence on symmetries in the intrinsic frame for collective nuclear models is analysed.

Shape phase transitions in even and odd systems are reviewed within the frameworks of the Interacting Boson Model(IBM) and the Interacting Boson Fermion Model(IBFM), respectively and compared with geometric models when available. We discuss, in particular, the case of an odd j = 3/2 particle coupled to an even-even boson core that undergoes a transition from the spherical limit U(5) to the γ-unstable limit O(6). Energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviors qualitatively similar to those of the even core and they agree qualitatively with the model based on the E(5/4) boson-fermion symmetry. We describe then the U^BF(5) to SU^BF(3) transition when a fermion is allowed to occupy the orbits j = 1/2, 3/2, 5/2. The additional particle characterizes the properties at the critical points in finite quantum systems.

Models of nuclear collective dynamics are used to study the interplay of order (approximate dynamical symmetry) and chaos in general physical systems. We report on some recent results obtained within the interacting boson model and the geometric model.

Following a series of experiments launched by the TetraNuc collaboration to possibly demonstrate the existence of high-rank symmetries in subatomic physics, the first experimental results on the Rare Earth region appear in publications. Meanwhile an important progress has been made on the theory side strongly suggesting that the original criterion of the static tetrahedral symmetry in the form of vanishing quadrupole moments may need to be revised to include explicitly the vibrational motion. The Actinide region seems of particular interest because of the extra stability provided by the octahedral symmetry. In this article a summary of the current experimental efforts on both the Rare-Earth and Actinide regions is given. Finally the ELMA project addressing the experimental search for the symmetries in the Actinides is briefly discussed.

Effects of the parity-mixed single-particle (s.p.) state on the collective properties of odd nuclei with reflection-asymmetric degrees of freedom are studied. The Coriolis strength and the average s.p. parity in the nuclei ²¹⁹Ra, ²²⁵Ra, ²²⁵Th and ²⁴¹Cm are examined in dependence on axial quadrupole and octupole deformation parameters β₂ and β₃ within a reflection-asymmetric deformed shell model. The obtained behaviour of the Coriolis decoupling factor in the (β₂, β₃)-plane is compared with values fitted in a collective quadrupole-octupole model, which allows one to determine physically reasonable deformation regions for the considered nuclei. The study provides a relation between deformation parameters, Coriolis interaction strength and the structure of collective spectra in odd-mass nuclei with quadrupole-octupole deformations.

Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial deformations. In the second part we discuss a microscopic theory of quantum phase transitions (QPT) based on the relativistic generator coordinate method.

We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed β-decay rates in the vicinity of the N = Z line. A preliminary value obtained for the Cabibbo–Kobayashi–Maskawa matrix element, |V_ud| = 0.97463(24), agrees well with the recent estimate by Towner and Hardy [Phys. Rev.C77, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |T_z| = 1 nuclei around ²⁴Mg and ⁴⁸Cr, namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

We report the first application of a recently proposed regularization procedure for multi-reference energy density functionals, which removes spurious divergent or non-continuous contributions to the binding energy, to a general configuration mixing. As an example, we present a calculation that corresponds to the particle-number and angular momentum projection of axially symmetric time-reversal invariant quasiparticle vacua of different quadrupole deformation for the nucleus ¹⁸O. The SIII parameterization of the Skyrme energy functional is used.

We review the notion of symmetry breaking and restoration within the frame of nuclear energy density functional methods. We focus on key differences between wave-function-and energy-functional-based methods. In particular, we point to difficulties encountered within the energy functional framework and discuss new potential constraints on the underlying energy density functional that could make the restoration of broken symmetries better formulated within such a formalism. We refer to Ref.¹ for details.

Super-allowed 0⁺ → 0⁺ Fermi transitions provide a test at low energy of the Standard Model of elementary interactions. The isospin-symmetry breaking due to the electromagnetic interaction at a nuclear level is a fundamental theoretical tool for the understanding of weak processes beyond the Standard Model. Within the Higher Tamm–Dancoff description of correlated nuclear states, we calculate the isospin-symmetry breaking correction δ_c to the Fermi transition matrix element. A sensitivity study on the T = 0 pairing correlations is carried out and some tests of model ingredients are performed. The obtained correction is of the order of 0.15~0.2% for plausible strengths in the T = 1 and T = 0 channels of the residual interaction. This is expected to constitute a lower bound.

Low-energy E1 strength in neutron-rich ^132-164Sn isotopes is analyzed in the framework of the Skyrme random phase approximation (RPA) with different Skyrme forces. A double folding procedure is applied to take into account the energy-dependent width effects beyond RPA. All the considered Skyrme forces indicate a soft prolate deformation in the open shell isotopes ^142-164Sn. The integrated E1 strength in the energy region of the pygmy resonance grows with the neutron number. The influence of deformation on the integrated strength near the particle emission thresholds (which is of a keen astrophysical interest) is strictly suppressed by the mutual compensation effect for the branches of the giant dipole resonance. The results obtained are in a good agreement with the previous findings of the relativistic mean field model.

The order-to-chaos transition in the dynamics of independent classical and quantum gas of particles was studied by means of the computer simulations within the nuclear model based on the time-dependent mean-field approach. The excitation of the classical gas for containers whose surfaces are rippled according to Legendre polynomials P₂, P₃ is followed for twenty periods of oscillations. For different vibration frequencies of small amplitude vibrations of such a container near the spherical equilibrium shape we obtained for the classical gas much smaller excitation energies than those predicted by the wall formula. With increasing equilibrium deformation they become significantly larger and for P₃ vibrations they are close to the wall formula limit. Notable shell effects were found in the excitation energies of the quantum gas in the Woods-Saxon potential with the corresponding relatively sharp (diffuseness equals to 0.1 fm) moving surfaces for small-amplitude slow vibrations.

Spinodal amplification provides a mechanism by which the spatial symmetry of an unstable system is broken as it spontaneously separates into its thermodynamically coexisting phases. This general phenomenon has been exploited to signal the nuclear liquid-gas phase structure in nuclear collision experiments at medium energies and it may also be of use in relativistic collisions for exploring the expected first-order confinement transition.

A complete set of 27 excitation functions for synthesis of superheavy nuclei produced in cold fusion reactions was analyzed in terms of the "Fusion by Diffusion Model" of Światecki et al., modified to account for the angular momentum dependence of the fusion hindrance factor. The data on cold fusion reactions originate from experiments carried out at GSI Darmstadt, RIKEN Tokyo and LBNL Berkeley in which ²⁰⁸Pb and ²⁰⁹Bi targets were bombarded with the variety of projectiles ranging from ^48,50Ti to ⁷⁰Zn.

The Strutinsky shell correction and the pairing correlations at deformations close to scission point are studied. It is shown that the shell correction energy of the nuclear system at scission is simply the sum of the shell-correction energies of the two nascent fragments while this is not the case for the pairing corrections when the reflection symmetry of the system is broken. To study this effect the use of a δ-pairing force or of the Gogny interaction is recommended. It is also shown that the strength of the pairing correlations should grow with increasing deformation of the fissioning nucleus in order to obtain the correct properties of the fragments.

The inaccuracy of calculated masses M and (static) fission-barrier height of heaviest nuclei is estimated. The estimation is performed within a macroscopic-microscopic approach for two nuclei: a heavy nucleus ²⁵⁰Cf and a superheavy one ²⁹⁴118. The source of the inaccuracy is the inaccuracy of calculated deformation of a nucleus and of calculated pairing-interaction strength. It is shown that the inaccuracy of the ground-state mass M, due to the inaccuracy of the calculated deformation is small, up to about 20 keV. The inaccuracy of M, due to the inaccuracy of the pairing strength is much larger, up to 310 keV. The inaccuracy of , due to the inaccuracy of the deformation is up to about 70 keV, while this due to the inaccuracy of the pairing strength is up to 520 keV. For both studied nuclei, the calculated inaccuracy of is smaller than the discrepancy between the values of obtained recently within different macroscopic-microscopic models.

The Poincaré instability of saddle-point shapes with respect to reflection asymmetric distortions is investigated for a series of light nuclei in the framework of the Lublin-Strasbourg drop model and the Modified Funny-Hills shape parametrization. It turn out that such a decay caused by this effect will only occur in rather strongly thermally excited, rotating nuclei.

The theoretical and experimental progress following the prediction of the chirality in nuclear physics in 1997 is reviewed. Possible existence of M_χD in ¹⁰⁵Rh is discussed.

First predictions for a specific case of the particle-hole-core coupling model which takes advantage of symmetries of a triaxial rotor with γ = 90° are reviewed. Results of the model calculations point towards existence of stable chiral geometry in specific configurations involving high-j orbitals. Next, experimental information on doublet bands built on unique parity, πh_11/2νh_11/2 intruder states in odd-odd ¹³⁴Pr is discussed; in particular observed disagreements between electromagnetic transitions within the doublet structures which is pointed out as inconsistent with the simplest models. Finally, the unique experimental infrastructure developed at the Tri-University Meson Facility (TRIUMF) Canada's National Laboratory for Particle and Nuclear Physics is presented including a range of isotopes in the mass 130 region that are accessible as beams and which can possibly yield significant new information in investigations of nuclear chirality.

The two-quasiparticle-plus-triaxial-rotor model was applied to study chiral configurations in the 100, 130 and 190 mass regions. It was shown that in order for a degeneracy in the two-quasiparticle partner bands to occur, one needs mutually orthogonal angular momenta of the odd proton, odd neutron and the collective rotation. The staggering in the B(M1) reduced transition probabilities as an indication of strongly broken symmetry was studied too.

An odd-odd nucleus is treated as the core-particle-hole system. The core is described by the Bohr Hamiltonian. Different collective potentials of the core are investigated. The odd particle and hole are assumed to be in the symmetric configuration. Signatures of chirality in the odd-odd nucleus spectra are observed. The sufficient condition for the appearance of signatures of chirality in the core-particle-hole system is the α-symmetry of the core provided the particle-hole configuration of the odd valence particles is symmetric.

In order to find the selection rules that can be applied to the electromagnetic transitions when the chiral geometry is achieved, a model for a special configuration in triaxial odd-odd nuclei is constructed which exhibits degenerate chiral bands with a sizable rotation. A quantum number obtained from the invariance of the Hamiltonian is given and the selection rule for electromagnetic transition probabilities in chiral bands is derived in terms of this quantum number. Among the available candidates for chiral bands of odd-odd nuclei, in which the near degeneracy of two ΔI = 1 bands is observed, the measured electromagnetic properties of the two bands in and are consistent with the rules, while those of and are not.

Nuclear chirality has been intensively studdied for the last several years in the context of experimental as well as theoretical approach. Characteristic gamma selection rules have been predicted for the strong chiral symmetry breaking limit that has been observed in Cs isotopes. The presented analysis shows that the gamma selection rules cannot be attributed only to chiral symmetry breaking. The selection rules relate to structural composition of the chiral rotational bands, i.e., to odd particle configuration and the deformation of the core.

Finite temperature Hartree-Fock-Bogoliubov calculations are performed in finite nuclei using Skyrme and zero-range, density-dependent pairing interactions. The value of the critical temperature follows approximatively the empirical rule T_c ≃ 0.5 Δ_T=0. The specific heat is calculated within the FT-HFB framework. Preliminary results obtained with the FT-QRPA are discussed.

General aspect of microscopic cluster models based on the combination of the Generator-Coordinate-Method and of the R-matrix method are presented. The adequacy of such a method to describe cluster states and reactions of astrophysical interest is illustrated by two typical examples.

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the ħ → 0, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvment of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.

The role of the entrance channel in the formation of the reaction products is discussed. The excitation functions of evaporation residues for the ⁵⁰Ti+²⁴⁹Cf and ⁵⁴Cr+²⁴⁸Cm reactions are compared.

The light krypton isotopes were studied in a series of Coulomb excitation experiments using radioactive beams at GANIL. The static quadrupole moments found in these experiments give firm experimental evidence for the shape coexistence scenario that is based on theoretical calculations and on the systematics of low-lying excited 0⁺ states. The experimental results are interpreted within a phenomenological two-band mixing model. Configuration mixing calculations based on triaxial Hartree-Fock-Bogolyubov calculations with the Gogny D1S effective interaction have been performed and compared to experimental data.

A relationship between experimental E2 matrix elements and nuclear quadrupole charge deformation and triaxiality is presented. Examples of experimentally determined deformation and triaxiality parameters in various regions of the nuclear chart are specified. The most interesting results were found among transitional nuclei. The first such result from a radioactive beam facility is the identification of a triaxial strongly-deformed low-lying level in ⁷⁶Kr.

A global parameterization is presented for the electromagnetic strength in heavy nuclei which gives a rather good fit to respective data in nuclei with mass numbers A between 50 and 240. It relies on a Lorentzian description of the isovector giant dipole resonance and it needs only a very small number of parameters to describe the electric dipole strength down to low excitation energy of importance for radiative capture processes. The resonance energies are chosen to be in accordance to liquid drop model parameters adjusted to ground state masses and to rotation invariant determinations of ground state deformation and triaxiality. By a straightforward use of this information a surprisingly smooth variation of the GDR width with A and Z is found and a full agreement to the predictions of the electromagnetic sum rule is assured. Predictions for radiative neutron capture cross sections compare well to respective data, when the proposed photon strength function is combined with standard prescriptions for the level density in the product nuclei.

The quadrupole shape evolution in heaviest stable Mo isotopes is studied in terms of the shape coexistence phenomenon occurrence in this region of nuclear chart. Quadrupole deformation parameters of the ^96,98,100Mo isotopes in the low-lying (ground and excited) 0⁺ states were deduced using Coulomb excitation method. In all cases rich sets of electromagnetic reduced matrix elements were determined using the GOSIA code and then analysed using the Quadrupole Sum Rules formalism. Discussion of the experimental results in comparison with the predictions of microscopic calculations within the general quadrupole collective Bohr Hamiltonian model is presented for ¹⁰⁰Mo.

Neutrinoless double beta (0νββ) decay of ⁷⁶Ge to the ground state and first excited 0⁺ state in ⁷⁶Se is discussed in terms of the associated nuclear matrix elements. The effects arizing from the size of the single-particle model space and the occupancies of the individual orbits are discussed in the framework of the (higher) quasiparticle random-phase approximation with effective, G-matrix-derived nuclear forces. It is found that the orbital occupancies play a role for the size of the nuclear matrix element. Contrary to the ground-state transition the transition to the first excited 0⁺ state does not depend sensitively on the size of the model space.

A class of relativistic nuclear energy density functionals is explored, in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance correlations, as well as intermediate and long-range dynamics, are encoded in the nucleon-density dependence of the strength functionals of an effective interaction Lagrangian. The resulting phenomenological effective interaction, adjusted to experimental binding energies of a large set of axially deformed nuclei, together with a new separable pairing interaction adjusted to reproduce the pairing gap in nuclear matter calculated with the Gogny force, is applied in the description of the quadrupole dynamics in Pt isotopes.

The yrast states of nuclei that are spherical or weakly deformed in their ground states are described as quadrupole waves running over the nuclear surface, which we call "tidal waves". The energies and E2 transition probabilities of the yrast states in nuclides with Z= 44, 46, 48 and N= 56, 58,…, 66 are calculated by means of the cranking model in a microscopic way. The nonlinear response of the nucleonic orbitals results in a strong coupling between shape and single particle degrees of freedom.

A 985 MeV ¹⁷⁸Hf beam was Coulomb excited by a ²⁰⁸Pb target at the ATLAS accelerator of Argonne National Laboratory. Gammasphere and the CHICO particle detector recorded particle-γ coincidence data. The aim was to populate and determine the mechanism of previously observed Coulomb excitation of the K^π = 6⁺ (t_1/2 = 77 ns), 8^- (4 s) and 16⁺ (31 y) isomer bands. New rotational bands were identified including an aligned band which appears to mix with the ground-state band (GSB) and the γ-vibrational band above ~ 12 ħ of angular momentum. Newly observed γ-decay transitions into the three isomer bands may elucidate the K-mixing which allows Coulomb excitation of these isomer bands, but direct decays from the GSB into the 16⁺ isomer band have not yet been confirmed.

The recently developed model of three-dimensional angular momentum projection plus generator coordinate method on top of triaxial relativistic mean-field states has been applied to study the low-lying states of ³⁰Mg. The effects of triaxiality on the low-energy spectra and E0 and E2 transitions are examined.

Measurements of γ-ray cascades originating from radiative neutron capture in several deformed nuclei were performed using different experimental setups. Specifically, two-step γ cascades following the capture of thermal neutrons were measured at the Řež reactor, while multi-step γ cascades following the neutron capture were measured with 4π BaF₂ detectors at isolated resonances in Los Alamos and in unresolved resonance region in Karlsruhe. Experimental data from these experiments were analyzed within the statistical approach using the DICEBOX code. Results of the analysis indicate that the scissors mode of excited nuclei plays an important role in the γ decay of all the deformed nuclei studied. Properties of the mode seen from these experiments are discussed.

The sensitivity of the nuclear collectivity to the pairing strength in ¹⁵⁰Nd has been investigated in a collective Hamiltonian based on the relativistic point-coupling energy functional with the delta-pairing force. With the increasing pairing strength, the potential energy curve becomes shallower and softer, and the inertia parameters will be reduced rapidly. Correspondingly, the excited energies increase parabolically, but the characteristic collective observables, and transition decrease linearly.

We apply the standard collective nuclear Hamiltonian derived in the literature with the help of the Adiabatic Time Dependent Hartree-Fock (ATDHF) theory. We use a schematic two-dimensional collective space spanned by the axial-quadrupole (α₂₀) vs. tetrahedral (α₃₂) deformations together with the potential energy surfaces calculated microscopically. We illustrate and discuss the collective-model solutions suggesting that the tetrahedral-symmetry nuclei may generate sizeable quadrupole transitions: this result is in contrast to the previous expectations and/or predictions.

Neutrinos do oscillate, which up to our best knowledge implies that they are massive particles. As such, neutrinos should interact with gravitational fields. As their masses are tiny, the gravitational fields must be extremely strong. In this paper we study the influence of black holes described by non-trivial topologies on the neutrino oscillations. We present approximate analytical and numerical solutions of certain specific cases.

In the recent years an interesting suggestion has been made that nucleus, like many other quantum objects, can have tetrahedral shape at the ground state. We test this hypothesis within the macroscopic-microscopic method, by using a 12 dimensional manifold of shapes, including: axial, nonaxial and reflection-asymmetric ones. We systematically calculate potential energy surfaces for even-even heavy and superheavy nuclei in the range of proton numbers 82 ≤ Z ≤ 128 and neutron numbers 98 ≤ N ≤ 194. We find that in the whole region of the investigated superheavy nuclei, tetrahedral symmetry does not play a significant role at the ground state.

The high spin states of ⁷⁹Kr were studied via the ⁷⁰Zn(¹³C, 4n) reaction to search for chiral doublet bands based on the three-quasi-particle configuration, πg_9/2² ⊗ νg_9/2^-1. The ¹³C beam of 65 MeV was provided by the 930 AVF Cyclotron at CYclotron and RadioIsotope Center (CYRIC) facility at Tohoku University. The triple coincidence γ rays were detected by the Hyperball2 array. The side band structure to the πg_9/2² ⊗ νg_9/2^-1 yrast band has been identified in ⁷⁹Kr. Spin and parity assignments are made based on the DCO ratio and linear polarization analysis.

Spectra of two-step γ cascades (TSCs) following thermal neutron capture in ¹⁵⁹Tb were measured. In order to obtain information about the quantities governing the γ decay of ¹⁶⁰Tb - the photon strength functions and the level density - the experimental TSC spectra were compared with the outcome of simulations of the γ cascade decay based on the validity of the extreme statistical model. The results obtained lead to an inescapable conclusion that the M1 scissors vibrational mode plays a crucial role in the cascade γ decay of the product nucleus ¹⁶⁰Tb. This finding represents the first evidence for the existence of the scissors mode in an odd-odd nucleus.

The problem of describing spontaneous fission for the entire region of superheavy nuclei is continually present in theoretical investigations. This study outlines the results of the calculations of fission barriers and spontaneous fission half-lives for superheavy nuclei in the region of Z=100-122 using a mean field model. We examine four distinct macroscopic models and two types of pairing interactions. Our approach is based on the deformed Woods-Saxon potential. Spontaneous fission half-lives are calculated using a multi-dimensional dynamical-programming method, where the action integral is minimized within a three dimensional deformation space (β₂, β₄, β₆).

Masses and rotational energies of even-even Fm - Hs isotopes are obtained using the Yukawa-folded single-particle potential and the Lublin Strasbourg Drop . The Strutinsky shell-correction method and the BCS approximation were used to evaluate the shell and pairing corrections. The paring force strength is adjusted to the experimental rotational states of the considered nuclei. The ground-state masses and the lowest rotational states obtained by using the cranking moments of inertia at the equilibrium deformations agree well with the experimental data.

We present results of a new analysis of the experiment carried out by the REVERSE-ISOSPIN collaboration on the ¹²⁴Sn + ⁶⁴Ni reaction at the bombarding energy of 35 MeV/nucleon. The mass numbers of the intermediate mass fragments (isotopes of Be, B and C) could be resolved in this experiment. Angular distributions of the neck fragmentation products in the rest frame of the primary projectile-like fragment were studied. The angular dependence of the isotopic ratios of the intermediate mass fragments proves the effect of neutron enrichment of the neck region.

The nuclear fission phenomenon is a magnificent example of a quantal collective motion during which the nucleus evolves in a multidimensional space representing shapes with different geometries. The triaxial degrees of freedom are usually important around the inner fission barrier, and reduce the fission barrier height by several MeV. Beyond the inner barrier, reflection-asymmetric shapes corresponding to asymmetric elongated fragments come into play. We discuss the interplay between different symmetry breaking mechanisms in the case of even-even fermium isotopes using the Skyrme HFB formalism.

Nuclear fission barriers, mass parameters and spontaneous fission half lives of fermium isotopes calculated in a framework of the Skyrme Hartree-Fock-Bogoliubov model with the SkM* force are discussed. Zero-point energy corrections in the ground state are determined for each nucleus using the Gaussian overlap approximation of the generator coordinate method and in the cranking formalism. Results of spontaneous fission half lives are compared to experimental data.

The rotational basis for irreducible representations of the point groups T_d, O and O_h for nuclear angular momenta J = 0, 1…, 5 is constructed.

We report results of fully non-perturbative calculations, based on Auxiliary Field Quantum Monte Carlo (AFQMC) approach, for the dilute neutron matter at the density ρ = 0.003fm^-3. Fundamental quantities which characterize the superfluid state: the single particle energy gap Δ(T), and the critical temperature T_c have been determined. The large value of Δ(0)/T_c ≈ 3.2 indicates that the system is not a BCS-type superfluid at low temperatures.

The target-material dependence of the neutron-proton branching ratio and breaking of the isospin symmetry in the the ²H(d, n)³He and ²H(d, p)³H reactions at very low deuteron energies have been investigated. Angular distributions and total cross sections of the proton and neutron mirror channels have been measured for nuclear reactions taking place in different metallic environments. For Sr, Li, Na targets, we have found a first evidence for an alteration of the neutron-proton branching ratio and angular anisotropy of the neutron channel. We discuss various theoretical approaches explaining isospin mixing effects both in gas and metallic target experiments including a deuteron polarization in the crystal lattice. Direct reaction contribution has been calculated within the zero range distorted wave Born approximation (DWBA).