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1.
It is shown that a positive diatomic molecule consisting of N electrons and two nuclei with charges Z 1 and Z 2 is unstable with respect to breakup into two atomic subsystems if the nuclear charges are sufficiently large. Bounds on the critical charge are obtained in the limit as N .Research supported in part by NSF grants DMS-8709805 and DMS-8808112.  相似文献   

2.
General kinetic equations are derived for nuclear reactions in dense plasmas by taking into account first-order collective plasma effects. We show that, apart from the corrections proportional to the product of the charges Z i and Z j of two reacting nuclei i and j, new corrections comparable in magnitude and proportional to the squares of the nuclear charges Z i 2 and Z j 2 arise. The Salpeter corrections [1] to the nuclear reaction probabilities due to the plasma screening of the interaction potential are shown to be at least a factor of r/d (r is the nuclear size and d is the Debye screening length) smaller than those assumed previously. These are zero in the approximation where the terms of order r/d are disregarded. The correlation corrections proportional to Z iZj have a different physical meaning than those in [1], can have a different sign, and arise for reactions with zero Salpeter corrections. For the correlation corrections that substitute for the previously used Salpeter corrections, strong correlations are difficult to describe analytically. The interpolation formulas between weak and strong Salpeter screenings previously used in many astrophysical applications are inapplicable, because the interpolation formulas between weak and strong correlations cannot yet be obtained. We found a new type of corrections that are proportional to the squares of the charges of reacting nuclei. These are attributable to a change in the collective electrostatic self-energy of the plasma system during nuclear reactions. Plasma corrections for the hydrogen-cycle nuclear reactions are numerically calculated for the temperature, density, and abundances in the solar interior.  相似文献   

3.
We show that the spin-orbit potential of the nuclear mean field destroys isoscalar superfluid correlations in self-conjugate nuclei. Using group theory and boson mapping techniques on a Hamiltonian including single particle splittings and a SO ST(8) pairing interaction, we give analytical expressions for the spin-orbit dependence of some N = Z properties such as the relative position of T = 0 and T = 1 states in odd-odd systems or double binding-energy differences of even-even nuclei. Received: 12 April 2000 / Accepted: 25 May 2000  相似文献   

4.
Summary The hyperfine coupling between spin of electrons ins states and nuclear spin is generally represented by a contact Hamiltonian in which a δ(r) factor appears. Utilizing relativistic equations and considering pointlike nuclei, we show that the δ(r) factor must be replaced by a steeply decreasing radial function of half-maximum width δr=5.8·10−14Z cm. For hydrogen, the correction with respect to the contact Hamiltonian turns out to be small, but for high-Z nuclei this correction acquires substantial importance. For iron 1s states, it rises up to 9.6%.  相似文献   

5.
Assuming the Born-Oppenheimer (clamped nuclei) approximation, basic properties of the Dirac operator for homonuclear two-centre one-electron systems are studied. This includes a rigorous analysis of the regularity of the potential energy curves as a function of the internuclear distance; in particular, for all values of the nuclear charge parameter that guarantee existence of a physically reasonable self-adjoint extension of the corresponding atomic Dirac-Coulomb operator, the continuity and differentiability of the electronic contribution to the potential energy curves are shown also to hold in the united atom limit. Furthermore, for nuclear charges not too large, the ground state united atom energy is demonstrated to provide a universal lower bound to all molecular energies within the discrete spectrum. Together with a generalization of the virial theorem to diatomic Dirac-Coulomb operators, this leads to a lower bound on the equilibrium separation between the nuclei. In addition, by employing appropriate variational arguments, the possibility of molecular bonding (for sufficiently large nuclear mass) is proved for all systems with charges up to those of the hydrogen molecular ion H2+.  相似文献   

6.
We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, e 2, and the ultra-violet cut-off, Λ, and for all nuclear charges less than the critical charge without radiation field, Z c  = e −22/(2/π + π/2). We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of e 2 and Λ and for nuclear charges less than e −22/π.  相似文献   

7.
According to Order-Disorder Model (ODM), in the early stages of fission, the charges in a fissioning nucleus gets polarised into two impending parts along with corresponding most stable neutrons which are calculated from the minimum in isobaric mass parabola. This polarisation into two most stable configuration leaves a small number of neutrons as balance neutrons i.e.N bal. The distribution of theseN bal for various polarisation modes, shows a very profound correlation with the yield distribution. Judging from this striking correlation between these two distributions, it can be predicted that the asymmetry in fission decreases gradually and ultimately disappear for nuclei havingZ ⋍ 102 but reappears again for the nuclei in super heavy region.  相似文献   

8.
QICUN SHI  SABRE KAIS 《Molecular physics》2013,111(19):1485-1493
We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres, Z + e ?Z+. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Zc = 1.228279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.  相似文献   

9.
Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z 1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A 1/3 law. A delicate scattering of data around R c/Z 1/3 is inferred as owing to the isospin effect and a linear dependence of R c/Z 1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z 1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002  相似文献   

10.
The lower levels of the discrete spectrum of a hydrogen-like atom are calculated within the point-like nucleus approximation with nonperturbative consideration for the Schwinger interaction of the radiative component of the magnetic moment of a free electron with the Coulomb field of a nucleus. The behavior of the 1s 1/2, 2s 1/2, 2p 1/2, and 2p 3/2 levels is investigated depending on the nuclear charge values, including the range of Z > 137, where the Dirac Hamiltonian continues to be self adjoint in the presence of the Schwinger term. It is shown that the Schwinger interaction for large Z causes significant changes in the properties of the discrete spectrum; in particular, the first level that reaches the threshold of a negative continuum is 2p 1/2 and this occurs at Z = 147. The behavior of the g-factor of an electron for the 1s 1/2 and 2p 1/2 states as a function of Z is considered as well and it is shown that for extremely large charges the correction to the g-factor due to the Schwinger term becomes a very significant effect.  相似文献   

11.
The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.  相似文献   

12.
《Physics Reports》1998,294(4):167-263
We present nuclear reaction network calculations to investigate the influence of nuclear structure on the rp-process between Ge and Sn in various scenarios. Due to the lack of experimental data for neutron-deficient nuclei in this region, we discuss currently available model predictions for nuclear masses and deformations as well as methods of calculating reaction rates (Hauser-Feshbach) and β-decay rates (QRPA and shell model). In addition, we apply a valence nucleon (NpNn) correlation scheme for the prediction of masses and deformations. We also describe the calculations of 2p-capture reactions, which had not been considered before in this mass region. We find that in X-ray bursts 2p-capture reactions accelerate the reaction flow into the Z ≥ 36 region considerably. Therefore, the rp-process in most X-ray bursts does not end in the Z = 32–36 region as previously assumed and overproduction factors of 107–108 are reached for some light p-nuclei in the A = 80–100 region. This might be of interest in respect of the yet unexplained large observed solar system abundances of these nuclei. Nuclei in this region can also be produced via the rp-proces in accretion disks around low mass black holes. Our results indicate that the rp-process energy production in the Z > 32 region cannot be neglected in these scenarios. We discuss in detail the influence of the various nuclear structure input parameters and their current uncertainties on these results. It turns out that rp-process nucleosynthesis is mainly determined by nuclear masses and β-decay rates of nuclei along the proton drip line. We present a detailed list of nuclei for which mass or β-decay rate measurements would be crucial to further constrain the models.  相似文献   

13.
The matrix elements of the effective Hamiltonian in the 0g 9/2-1p 1/2 space are determined by a least-square fit to the energies of 477 levels of nuclei with 38≤Z≤50 and 47≤N≤50. The results of the calculation are found to be in better agreement with experiment than those obtained with previously determined interactions. Received: 31 May 2001 / Accepted: 14 June 2001  相似文献   

14.
We consider a large neutral molecule with total nuclear charge Z in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that Z α 2κ 0 for a sufficiently small κ 0, where α denotes the fine structure constant. We show that, in the simultaneous limit Z → ∞, α → 0 such that κZ α 2 is fixed, the ground state energy of the system is given by a two term expansion c 1 Z 7/3 + c 2(κ) Z 2 + o(Z 2). The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.  相似文献   

15.
The results of a calculation of the electron wave function for the critical state (? = ?mec2) and of some related quantities are presented. The effect of the finite nuclear size on the critical internuclear distance Rcr is taken into account. The calculations are performed by means of the variational method for nuclei with charges 85 ? Z ? 100. The error of the WKB method for strong Coulomb fields is found to be a few percent.  相似文献   

16.
The similarity of the abundance of heavy nuclei in the Universe with that of the nuclei produced in the fully reproducible reactions of protons in host metals like palladium, nickel or others is evident and can be described by the same exponential function of the distribution probability N(Z) depending on the proton number Z of the nuclides. This agrees with the earlier derived consequence of a 3 n relation for magic numbers and an alternative foundation of the nuclear shell model. Compared to femtometer-attosecond reactions in the big bang, the low energy nuclear reactions in the host metals have picometer distances and megasecond duration. For this picometer distance, a combination of the swimming electron layer and Debye screening model with a metal-plasma dielectric model is presented.  相似文献   

17.
We prove that in thed=2+1,U(1) Hamiltonian (continuous time) lattice gauge theory the confining potential between two static external charges grows logarithmically with their distance, at sufficiently high temperatures. As it is known that for zero or low temperatures and large coupling constant the model confines linearly, we have therefore established the existence of a Kosterlitz-Thouless transition. Our results are based on a Mermin-Wagner type of argument combined with correlation inequalities and known results for the two-dimensional (spin) Villain model.  相似文献   

18.
Neutron-deficient nuclei in the mass region A≈ 90-100 exhibit a large variety of phenomena. In this region the heaviest N = Z nuclei are identified and enhanced neutron-proton correlations are expected when protons and neutrons occupy identical orbitals. A variety of nuclear shapes are predicted and observed for A? 91, including superdeformed shapes. The nucleus 100Sn is the heaviest N = Z doubly magic nucleus believed to be bound. Knowledge of the shell structure around 100Sn is of utmost importance for understanding the nuclear shell model. New results on both the N = Z nucleus 88Ru, superdeformed structures in A≈ 90 nuclei as well as the first result on the level structure in 103Sn, and an extended level structure in 102In are presented. The limitations of using stable beams and targets and the possibilities with new radioactive beams are briefly outlined. Received: 1 May 2001 / Accepted: 4 December 2001  相似文献   

19.
    
The proton drip line defines one of the fundamental limits to nuclear stability. Nuclei lying beyond this line are energetically unbound to the emission of a constituent proton from their ground states. For near-spherical nuclei in the region of the drip line between Z=69 (Tm) and Z=81 (T1), proton decay transition rates have been shown to be well reproduced by WKB calculations using spectroscopic factors derived from a low-seniority shell model calculation [2]. Another approach using spectroscopic factors obtained from the independent quasiparticle approximation has also proved successful in this region [3]. These interpretations have allowed the extraction of nuclear structure information from nuclei well beyond the proton drip line. The rare-earth proton emitters 141Ho and 131Eu have recently been observed [4], and their decay rates can only be explained by assuming large deformation for these nuclei. In addition to providing information on the wavefunctions and deformations of these nuclei, these results offer the opportunity to study the phenomenon of quantum mechanical tunneling through a deformed potential barrier. Work supported by the U.S. Department of Energy, Nuclear Physics Division, under contract W-31-109-ENG-38.  相似文献   

20.
A class of A-nucleon (for even N = Z) Hamiltonians is found such that they admit, among others, solutions that can be exactly related to solutions to the problem of A/4 alpha particles in the sense that the respective eigenvalues of the two problems coincide and that the A-nucleon solutions can be constructed from the alpha-particle solutions within a procedure that follows from the resonating-group model. It is shown that an effective nuclear Hamiltonian close to a realistic one possesses these properties, the alpha-particle states in nuclei having basic properties of an alpha condensate and, frequently, a normal nuclear density. The statistics of alpha particles (and other composite bosons) proves to be different from Bose-Einstein and Fermi-Dirac statistics and from parastatistics.  相似文献   

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