Showing papers by "Jilin University published in 1982"

Control of spurious modes in the nine‐node quadrilateral element

Abstract: The nine-node quadrilateral is much more accurate than its eight-node relative if elements are non-rectangular. However, the nine-node element may display spurious low-energy modes under 2 × 2 Gauss quadrature. These modes can be controlled by using the 3 × 3 quadrature rule, but at added cost. This paper investigates two inexpensive control devices that can be used with 2 × 2 Gauss quadrature.

Matrix representation and estimations of remainder term of many-knot spline interpolating curves and surfaces

Abstract: Many-knot spline interpolation is a new class of curve and surface fitting method,created by the author in 1974. Many-knot spline is suitable to Computer Aided Geo-metrie Design and handling problems for some data. In this paper the matrix forms of representation of interpolating function are con-sidered, the estimations of remainder term for quadratic and cubic many-knot splineare given: ||R_2~((l))(x)|| = O(h~(3--1)), l = 0, 1, 2and ||R_3~((l))(x)|| = O(h~(4--1)), l = 0, 1, 2, 3.

The Composite Particle Representation Theory: (I) The Composite Particle Representation Transformation

Abstract: A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a generalized transformation. Using this generalization, we were able to construct a special representation called the "Composite Particle Representation". In the composite, particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical representation which includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons from the quark point of view and the Interacting Boson Model in nuclei.

Hyperfine-structure Study of the 72p3/2,82p3/2 and 92p3/2 States In Na-23 Using Quantum-beat Spectroscopy

Abstract: We have performed hyperfine-structure measurements on the 7, 8 and 9 2P3/2 states in 23Na using quantum-beat spectroscopy. The light from a pulsed dye laser, pumped by an excimer laser, was frequency-doubled and used to excite sodium atoms in an atomic beam. The fluorescence light was recorded by a transient digitizer and the transients were added in a digital memory and transferred to a mini-computer for calculations. For the magnetic-dipole and electric-quadrupole constants, a and b, we have obtained the following values: 7 2P3/2; a = 0.82(1) MHz, b = 0.13(3)MHz 8 2P3/2; a = 0.535(15) MHz, b = 0.070(25)MHz 9 2P3/2; a = 0.36(1) MHz, b = 0.045(15)MHz

An error estimate for theH −1 Galerkin method for a parabolic problem with non-smooth initial data

Abstract: A non-smooth data error estimate with respect to theL 2 norm is shown for a semidiscrete Galerkin-Petrov method for a parabolic problem in one space dimension. If the trial and test spaces consist of piecewise polynomials of degreer−1 inC k anr+1 inC k+2 , respectively, with test functions satisfying boundary conditions, then the error norm is bounded byCh r t −r/2 fort positive, whereh is the maximum mesh size.

Theory of Nuclear Single Particle Potential

Abstract: The single particle (sp) potential uαβ=Mαβ(eβ) [or Mαβ(eα)] defined in terms of the mass operator Mαβ(ω) is investigated in detail. First it is proven that although uαβ is non-hermitian, the energy eigen values of the single particle Schrodinger equation $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{h} |\gamma > {\text{ = }}(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{t} + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{u} )|\gamma > {\text{ }} = {\text{ }}\varepsilon _\gamma |\gamma > $$ are all real and satisfy rigorously the relation $$ \varepsilon _\gamma = \pm [E_\gamma (A \pm 1) - E_0 (A)] $$ where EO(A) denotes the exact ground state energy of a closed shell nucleus (A), Eγ(A±1) are exact energy eigenvalues of its neighboring nuclei of mass number A±1, and the upper (lower) sign holds if γ refers to a particle (hole) state. Then the principle of maximal cancellation of perturbation diagrams is analyzed by a new and non-perturbative method, which not only tells what terms can be cancelled by u [referred to as the cancellation property of u], but also yields an analytic expression for the remaining terms. It is proved that the cancellation property of u can be expressed analytically in the form $$ M_{\alpha \beta } (\varepsilon _\beta ){\text{ }} = {\text{ }}0, $$ where Mαβ(ω) is the reducible mass operator. The consequence of the above relation is studied. It is shown that the terms which can be cancelled by u are more plentiful than what were known previously. Further, it is discussed under what conditions the following approximation for Gαβ(t) holds $$ \begin{array}{*{20}{c}} {{G_{{p\beta }}}\left( {t > 0} \right) \simeq {A_{{p\beta }}}{e^{{ - i\varepsilon }}}{p^{t}}} \\ {{G_{{h\beta }}}\left( {t 0} \right) \simeq 0} \\ \end{array} $$ where Aαβ [referred to as amplitude renormalization factor] is rigorously given by $$ \begin{array}{*{20}c} {A_{\alpha \alpha } = 1 - [\frac{d} {{d\omega }}M_{\alpha \alpha } (\omega )]_{\omega = \varepsilon _\alpha } = 1 - M{\text{'}}_{\alpha \alpha } (\varepsilon _\alpha )} \\ {A_{\alpha \beta } = M_{\alpha \beta } (\varepsilon _\alpha )G_\beta ^o (\varepsilon _\alpha ),{\text{ }}(\alpha e \beta )} \\ \end{array}$$ and α, β may denote either a particle (p) or a hole (h) state. Finally a method for the calculation of Aαβ is suggested. One obtains, for instance, \({A_{{\alpha \alpha }}} = 1 - M_{{\alpha \alpha }}^{\prime }({\varepsilon _{\alpha }}){\text{ = }}{[{\text{1 - }}M_{{\alpha \alpha }}^{\prime }({\varepsilon _{\alpha }}){\text{ - }}\mathop{\Sigma }\limits_{{\gamma e \alpha }} {{\text{x}}_{{\alpha \gamma }}}{\text{G}}_{\gamma }^{{\text{o}}}({\varepsilon _{\alpha }}){{\text{M'}}_{{\gamma \alpha }}}({\varepsilon _{\alpha }})]^{{{\text{ - 1}}}}}\), which is reduced to the well known Brandow formula, if one neglects the non-diagonal elements and introduced the following approximation for \(M_{\alpha \alpha } (\omega ):M_{\alpha \alpha } (\omega ) \simeq \Sigma _h G_B (\alpha _h ,\alpha _h ;\omega + \varepsilon _h )A_{hh} \), where GB is Brueckner’s G-matrix.

Application of the Boson-Fermion Hybrid Representation: Why is Spin-Polarized Atomic Hydrogen a Bosonic System?

Abstract: In the previous talk by Wu1, a formalism known as the boson-fermion hybrid representation (BFHR) was proposed. The BFHR was utilized to form a theoretical foundation of the nuclear field theory2 (NFT). However, one must bear in mind that the interplay of bosons and fermions is by no means a mere nuclear phenomena, it is displayed in many other disciplines of physics as well. Therefore, if the BFHR is a general quantum mechanical representation, it can be utilized to study other physical systems which display this kind of intricate and fundamental phenomena. In this paper, we shall present the use of the BFHR in the case of the spin-polarized atomic hydrogen system.

The Boson Fermion-Hybrid Representation and the Nuclear Field Theory

Abstract: Mottelson in 19681 proposed the ideas of a nuclear field theory (NFT) as a theoretical scheme to treat the collective (Phonon pr particle-hole) and single-particle modes (fields) coupling. This theory was subsequently proliferated by the Copenhagen — Buenos Aires group into a diagrammatic perturbation theory (DPT)2. The central theme of the DPT is to introduce a set of “empirical” rules for the evaluation of the NFT diagrams.