Variational method for excited states from supersymmetric techniques

2003 ◽  
Vol 81 (11) ◽  
pp. 1283-1291 ◽  
Author(s):  
G RP Borges ◽  
A de Souza Dutra ◽  
Elso Drigo ◽  
J R Ruggiero
Keyword(s):  
Variational Method ◽  
Numerical Integration ◽  
Excited States ◽  
Ground State ◽  
Potential Parameter ◽  
The One ◽  
Double Well Potential ◽  
Good Agreement ◽  
03.65 Ge

We suggest a method for constructing trial eigenfunctions for excited states to be used in the variational method. This method is a generalization of the one that uses a superpotential to obtain the trial functions for the ground state. The construction of an effective hierarchy of Hamiltonians is used to determine excited variational energies. The first four eigenvalues for a quartic double-well potential are calculated for several values of the potential parameter. The results are in very good agreement with the eigenvalues obtained by numerical integration. PACS Nos.: 11.30.Pb, 03.65.Ge

Studies of nuclear collisions involving 8 MeV deuterons by the photographic method II. The energy of the excited states of 17 O

1951 ◽  
Vol 209 (1099) ◽  
pp. 478-488 ◽  
Keyword(s):  
Excited States ◽  
Ground State ◽  
Primary Beam ◽  
Photographic Method ◽  
Nuclear Collisions ◽  
Good Agreement ◽  
Α Particles

The apparatus described in part I has been employed to determine the energy of the excited states of the nucleus 17 O by observations on the protons from the reaction 16 O ( d , p ) 17 O, and on the α-particles from the reaction 19 F( d , α) 17 O . The protons from the first reaction were observed a t five angles of emission with respect to the primary beam, and the α-particles from the second at four angles. Thirteen excited states of 17 O were observed, evidence for ten of which was given by both reactions. The values for the energy in the different excited states, derived from both reactions and at different angles of observation, are in good agreement. The Q -values of the reactions 16 O( d , p ) 17 O and 19 F( d , α) 17 O , in which the 17 O nucleus is formed in its ground state, are 1.928 and 10.042 MeV, respectively. The Q -value for the reaction 16 O( d , α) 14 N was found to be 3.09 MeV, and the existence of two excited states of 14 N was established. Ten excited states of 20 F were observed in a study of the proton groups from the reaction 19 F( d , p ) 20 F.

scholarly journals Determination of GT-transition Strengths in \(A=34\) Isobars Using Charge Exchange \((^3\text{He},t)\) Reaction

2012 ◽  
Vol 22 (1) ◽  
pp. 91-96
Author(s):  
Nguyen Tuan Khai ◽  
Bui Duy Linh ◽  
Tran Duc Thiep ◽  
Y. Fujita ◽  
T Adachi ◽  
...  
Keyword(s):  
Excitation Energy ◽  
Excited States ◽  
Ground State ◽  
Incident Energy ◽  
High Energy ◽  
High Energy Resolution ◽  
Good Quantum Number ◽  
Gamow Teller ◽  
Good Agreement

Under the assumption that isospin \(T\) is a good quantum number, mirror transitions \(T_{z }= +1 \to  0\) and \(T_{z }= -1  \to  0\) were studied in \(A = 34\) isobars, where \(T_{z}\) is \(z\) component of iospin \(T\) and is defined by \(T_{z} = (N-Z)/2\). With a high energy resolution of 35 keV in \(^{34}\)S\((^{3}He,t)^{34}\)Cl reaction measurement at \(0^{\circ}\) scattering angle and at an incident energy of 140 MeV/nucleon, strengths of Fermi and Gamow-Teller (GT) transitions from the \(J^{\pi } = 0^{ + }\), \(T_{z }= +1\) ground state of \(^{34}\)S to the \(J^{\pi } = 1^{+ }\), \(T_{z }= 0\) excited states in \(^{34}\)Cl were determined up to excitation energy \((E_{x})\) of \(7.08\) MeV. The corresponding isospin-symmetric transitions connecting \(T_{z }= -1\) and \(T_{z }= 0\) states can be studied in the \(^{34}\)Ar \(\beta ^{ + }\) decay. The strengths of the \((GT)_{\pm }\) transitions were compared up to the excitation energy of 3.1 MeV. A good agreement was observed for two strong transitions to \(2.580\) MeV and \(3.129\) MeV states, while a disagreement about \(45\text{%}\) was observed for a weaker transition to \(0.666\) MeV low-lying state.

scholarly journals Electron Scattering from the Ground and Excited States of Barium

1999 ◽  
Vol 52 (3) ◽  
pp. 603
Author(s):  
Dmitry V. Fursa
Keyword(s):  
Excited States ◽  
Electron Scattering ◽  
Cross Sections ◽  
Differential Cross ◽  
Ground State ◽  
Differential Cross Sections ◽  
Close Coupling ◽  
Angular Correlations ◽  
Electron Photon ◽  
Good Agreement

We have used the nonrelativistic convergent close-coupling (CCC) method to investigate electron scattering from the ground (6s2)1S state and excited (6s6p)1 Po1 and (6s5d)1,3De2 states of barium. For the scattering from the barium ground state, we have found very good agreement with measurements of (6s6p)1 Po1 apparent cross sections at all energies. Similarly, good agreement is found for differential cross sections for elastic scattering and (6s6p)1 Po and (6s5d)1 De2 excitations and with the (6s6p)1 Po1 state electron{photon angular correlations. For the scattering from excited states of barium we have found good agreement with elastic (6s6p)1 Po1 scattering and the (6s5d)1De2 → (6s6p)1 Po1 transition for both differential cross sections and electron–photon angular correlations.

An Exciton Approach to the Excited States of Two Electron Atoms. II. Determination of Spectroscopic Parameters, Polarizabilities and Dispersion Coefficients of H-, He, Li+, Be2+ and Ne8+

1985 ◽  
Vol 38 (1) ◽  
pp. 11
Author(s):  
PE Schipper ◽  
B Martire
Keyword(s):  
Excited States ◽  
Ground State ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Exciton Model ◽  
Interaction Coefficients ◽  
Isoelectronic Series ◽  
Helium Isoelectronic Series ◽  
Good Agreement

The exciton model developed in an earlier paper is applied quantitatively to a description of the excited states of representative members of the helium isoelectronic series; viz. H-, He, Li+,Be2+ and Ne8+. The energies of the eight lowest excited states are in good agreement with experiment, for a relatively small (1s-4p) hydrogenic basis; the ground state is obtained with slightly less precision. Response properties including oscillator strengths, polarizabilities and dispersion interaction coefficients are also calculated. The method appears to be quantitatively sound, and, above all, leads to particularly simple interpretations of the wave functions and the energies.

Über das unterschiedliche Ionisationsgleichgewicht wasserstoff- und alkali-ähnlicher Ionen in optisch dünnen Plasmen

1967 ◽  
Vol 22 (12) ◽  
pp. 1939-1952
Author(s):  
C. Mahn
Keyword(s):  
Excited States ◽  
Ground State ◽  
Local Thermal Equilibrium ◽  
Radiation Absorption ◽  
Electron Densities ◽  
Recombination Processes ◽  
Ionization Limit ◽  
Energy States ◽  
The One ◽  
Collisional Ionization

There are many plasmas in which the populations of the various energy states of ions and electrons assume a steady state, but complete local thermal equilibrium is prevented because, on the one hand, radiation absorption is absent and, on the other, the electron density is too low.Calculations for a plasma without radiation absorption show that: Where hydrogen-like ions are involved it is nearly in order to dispense with detailed calculations and described the ionization equilibrium with the assumption that the collisional ionization processes from the ground state can be equated with the radiative recombination processes to the ground state. For sufficiently low electron densities this leads to the Corona formula.In the case of other ions, however, neglecting the excited states may result in serious errors. This is because these energy states — unlike those for hydrogen-like ions, which are relatively near the ionization limit — are distributed much more uniformly between the ground state and ionization limit. The implications of this behaviour are discussed with reference to alkali-like ions. A model for the term systems and the collision and radiation coefficients is used to derive the population densities and approximative ionization formulae. According to these the ratio of the densities of the lithium-like O VI ions and the next higher level of ions (O VII), for instance, may differ (for electron densities ne = 5 × 1017 cm–3) from the result of the Corona formula by a factor of 20.

The Microwave Spectrum of trans-2,3-Dimethyloxirane in Torsional Excited States

1996 ◽  
Vol 51 (8) ◽  
pp. 923-932 ◽  
Author(s):  
H. Hartwig ◽  
H. Dreizler
Keyword(s):  
Internal Rotation ◽  
Potential Function ◽  
Excited States ◽  
Ground State ◽  
Microwave Spectrum ◽  
Rotation Axes ◽  
Direction Cosines ◽  
Rotational Transitions ◽  
Good Agreement

Abstract The microwave spectrum of trans-2,3-dimethyloxirane (CH3CHOCHCH3) in the excited tor-sional states υ17 = 1 and υ33 = 1 has been measured in the range from 8 to 26 GHz and assigned. An analysis of internal rotation splittings of the observed rotational transitions was performed using the internal axis method (or "combined axis method") with a newly developed program accounting for the top-top coupling. The threefold hindering potential V3 and the direction cosines λ g,i of the internal rotation axes i with respect to the principal inertia axes g are in a good agreement with the ground state values. Additionally, the sixfold hindering parameter V6 was found to be - 0.2600(12) kJ/mol. The value of the parameter V′12 describing the top-top coupling in the potential function (via V′12 sin 3 τ1 sin 3 τ2), was determined to -0.4240(6) kJ/mol.

Relativistic Ground and Excited State Energies of a/1-Particle in Hypernuclei Using Woods-Saxon Potentials

1989 ◽  
Vol 44 (12) ◽  
pp. 1234-1238 ◽  
Author(s):  
C. G. Koutroulos
Keyword(s):  
Excited State ◽  
Dirac Equation ◽  
Excited States ◽  
Ground State ◽  
Scalar Potential ◽  
Binding Energies ◽  
Fitting Procedure ◽  
Fourth Component ◽  
Potential Parameters ◽  
Good Agreement

Abstract The relativistic Dirac equation with a scalar potential and the fourth component of a vector potential of the Woods-Saxon shape is solved numerically for potential parameters obtained by a last squares fitting procedure of the ground state binding energies of the Λ in a number of hypernuclei and its binding energies in the ground and excited states (as well as the relevant spacings) for various hypcrnuclei are determined. The results are in very good agreement with the preliminary experimental ones given by Chrien on the basis of the (π+, K+) reaction on nuclei.

Torsions-Vibrations-Rotations-Wechselwirkung im Mikrowellenspektrum von Methylthiocyanat

1974 ◽  
Vol 29 (5) ◽  
pp. 797-803 ◽  
Author(s):  
U. Andresen ◽  
H. Dreizier
Keyword(s):  
Ground State ◽  
Vibrational State ◽  
Degrees Of Freedom ◽  
Molecular Model ◽  
Microwave Spectrum ◽  
Potential Parameter ◽  
Pure Torsion ◽  
Excited Vibrational State ◽  
The Absolute ◽  
Good Agreement

Abstract The microwave spectrum of methylthiocyanate is reinvestigated on the basis of a molecular model with five degrees of freedom, three for the overall rotation, one for the torsion and one for another vibration. It was possible to fit the splittings of all four measured states (ground state, first excited torsional and vibrational state and second excited vibrational state) with one set of parameters but it was impossible to fit the absolute line frequencies. The value for the potential parameter of the pure torsion V3 is in good agreement with that determined on the basis of the rigid framerigid top (RF-RT) model from the ground state.

scholarly journals On the heat of sublimation of carbon and on some absorption bands of three mesomeric hydrocarbons

1941 ◽  
Vol 179 (977) ◽  
pp. 214-231 ◽  
Keyword(s):  
Excited State ◽  
Excited States ◽  
Internuclear Distance ◽  
Ground State ◽  
Spectroscopic Analysis ◽  
Breathing Frequency ◽  
Absorption Bands ◽  
Exact Agreement ◽  
Internuclear Distances ◽  
The One

Spectroscopic analysis of the CO spectrum , together with thermochemical measurements on the burning of carbon in oxygen, lead to the conclusion that L , the heat of sublimation of carbon, is either 124 or 170 kcal./mol. An estimate of L may be made by calculating the energies of excited states of benzene, butadiene and hexatriene, assuming various values of L , and choosing the one that gives the best agreement with experiment. The theory employed bears a close resemblance to that developed by Eyring for estimating activation energies. Almost exact agreement with experiment is obtained in all three cases by assuming L =170, and no agreement is obtained by assuming L = 124. More elaborate calculations are most unlikely to upset this result. The conclusion is therefore that L = 170 kcal./mol. The equilibrium internuclear distances in the excited states are found, and the potential function controlling some of the vibrations about these positions is determined. It is shown that the excited state of benzene has the regular hexagon configuration, the carbon-carbon internuclear distance being 1.45 A, compared with 1.39 in the ground state. The carbon breathing frequency in the excited state is calculated to be 920 cm. -1 , compared with the experimental value 940 cm. -1 .

Theoretical relativistic oscillator strengths I. Transitions in principal, sharp, and diffuse series of Al I, Ga I, In I, and Tl I spectra

1976 ◽  
Vol 54 (2) ◽  
pp. 118-129 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Experimental Data ◽  
Excited States ◽  
Principal Series ◽  
Semiempirical Method ◽  
Oscillator Strengths ◽  
Relative Line ◽  
Exchange Effects ◽  
The One ◽  
Relativistic Oscillator ◽  
Good Agreement

The oscillator strengths for the sharp, principal, and diffuse series in the spectra of Al I, Ga I, In I, and Tl I are calculated as well as the lifetimes of their lowest excited states. The wave functions that were used were calculated by employing a relativistic semiempirical method which included exchange effects. Very good agreement with the most reliable experimental data was obtained for the fik values in the sharp series as well as for the calculated lifetimes. The discrepancies in the diffuse series are ascribed to the failure of the one-electron approach in the case of strongly perturbed series. The observed deviations in the relative line strengths from the values predicted neglecting the spin–orbit interaction were also investigated. Some systematic trends in the calculated oscillator strengths that were found for the sharp and principal series appear to be corroborated by experimental data for the sharp series in the spectra of Al I, Ga 1, In I.andTl 1.

Sign in / Sign up

Export Citation Format

Share Document