Tamm-Dancoff Method Research Articles

Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations

The Light-Front Tamm-Dancoff method of finding the nonperturbative solutions in field theory is based on the Fock decomposition of the state vector, complemented with the sector-dependent nonperturbative renormalization scheme. We show in detail how to implement the renormalization procedure and to solve the simplest nontrivial example of the scalar Yukawa model in the two- and three-body Fock space truncations incorporating scalar "nucleon" and one or two scalar "pions".

Analysis of a QCD Hamiltonian in the low energy regime.

We present a QCD motivated Hamiltonian for the light quark sector. Inspired from self-consistent analysis of the Coulomb interaction, we implement an interaction of the form (-a/r + br) between color sources, which already consider gluonic dynamics by the linear potential contribution. A prediagonalization of the kinetic energy term followed by the implementation of the Tamm-Dancoff method are used to obtain the eigenvalues of the Hamiltonian. A variational analysis is implemented to obtain the optimized basis for the low energy meson spectrum. The potential parameter is compared to the reported lattice string tension with relatively good agreement. The obtained energies are located close to the experimental values and further improvements are discussed.

Microscopic Calculations for O(6) Nuclei by the Interacting Boson Model

We present microscopic calculations of the Interacting Boson Model (IBM) based on the shell model interaction by using the OAI mapping approach. We determine the collective pairs, which correspond to the IBM bosons, by the number conserved Hartree-Fock-Bogoluibov (HFB) and the proton-neutron Tamm-Dancoff methods, and we take into consideration couplings to the non-collective degrees of freedom. The present realistic calculations are carried out for the Te, Xe and Ba isotopes. Among them, the Xe isotopes are known by numerous phenomenological works to show the O(6) symmetry. We present the clear O(6) symmetry in the spectra and the wave function which are microscopically obtained.

Zero field splitting of triplet levels of conjugated molecules: A comparison of exact and approximate π-schemes

An exact method (full configuration interaction) and approximate schemes for the calculation of the anisotropy spin coupling matrix and the corresponding zero field splitting D parameter are considered. Calculation algorithms for the exact method and a special case (valence bond (VB) method) are also presented. The results of specific π calculations give evidence that the VB method in fact cannot be recommended for the description of the spin-spin interaction, especially for biradicals with the triplet ground state. At the same time, the Tamm-Dancoff method (taking into account all singly excited configurations) provides on average a good approximation to an accurate description of non-degenerate triplet states. The description of fine spin effects, which is rougher, but better than that in VB, is given by the restricted Hartree-Fock method for open shells.

Accurate Theoretical Description of the (1)La and (1)Lb Excited States in Acenes Using the All Order Constricted Variational Density Functional Theory Method and the Local Density Approximation.

We present the results of calculations on the vertical singlet (1)La and (1)Lb excitation energies in acenes within time dependent density functional theory (TDDFT), second order constricted variational DFT (CV(2)-DFT), and all order constricted variational DFT (CV(∞)-DFT) using the local density approximation LDA(VWN). For the linear acenes it is shown that the application of the Tamm-Dancoff (TD) approximation to TDDFT (TDDFT-TD) substantially improves the agreement with experiment compared to pure TDDFT. This improvement leads to the correct ordering of the (1)La and (1)Lb excitation energies in naphthalene. As TDDFT-TD is equivalent to the second order CV(2)-TD method one might hope for further improvements by going to all orders in CV(∞)-TD. Indeed, for linear acenes the application of the CV(∞)-TD method brings the agreement with experiment to within 0.1 eV for both types of excitations using the simple LDA functional. The CV(∞)-TD method based on LDA is also shown to be accurate for 15 nonlinear acenes with root-mean-square deviations of 0.24 eV for (1)La and 0.17 eV for (1)Lb.

Photodetachment cross section of lithium negative ion

The Relativistic Random Phase Approximation (RRPA) and the Multi-Configuration Tamm-Dancoff (MCTD) method have been used to obtain low-energy photodetachment cross-section of the Li- ion.

Level-dependent new tamm-dancoff calculations

Excitation energies using the level-dependent new Tamm-Dancoff method are calculated for four one-dimensional symmetric anharmonic oscillators. Convergence of the calculated excitations is demonstrated numerically and compared with the excitations obtained by integrating Schrodinger's equation numerically. The treatment is developed to illustrate how expansions other than level-dependent Wick expansions may be used to transform the T-recursion system into the π-recursion system. Specifically, numerical results for adjacent energy level differences for the sixth-degree oscillator are obtained using numerical solutions of the fourth-degree oscillator to construct the transformation that carries the T-recursion system into a π-recursion system.

Behram N. Kursunoglu

Behram N. Kursunoglu

Antisymmetric distorted wave impulse approximation calculations of spin transfer cross sections for(3He→,t→)reactions to the continuum

A formalism is presented for the calculation of spin transfer cross section for intermediate energy charge exchange ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ [and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})]$ reactions to the continuum. The nuclear structure part of the formalism is based on the continuum Tamm-Dancoff method and the nuclear reaction part is treated within the distorted wave impulse approximation. In the nuclear structure part, we thus include particle-hole correlations and continuum effects on the excited particle. The knockon-exchange effect and the damping of the particle through an imaginary potential added to the single particle real potential are also taken into account. Results of numerical calculations are presented for the inclusive cross sections $\ensuremath{\sigma}(0\ifmmode^\circ\else\textdegree\fi{})$ and the spin transfer coefficients ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for forward scattering, for the intermediate energy ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})$ reactions on ${}^{12}\mathrm{C}$ and ${}^{90}\mathrm{Zr}$ targets leading to Gamow-Teller resonances in the continuum. It is shown that ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for this case takes a value of $\ensuremath{-}1/3,$ regardless of the details of nuclear structure and reaction mechanisms, if the reaction is assumed to proceed as an orbital angular momentum transfer ${l}_{t}=0$ process, and that deviations from $\ensuremath{-}1/3$ come from admixture of ${l}_{t}=2$ components. A simple closed form of the expression is derived which can be used to understand a subtle dependence of the ${D}_{\mathrm{nn}}$ values on nuclear structure and effective interaction.

Chiral quark model in a Tamm-Dancoff inspired approximation

A procedure inspired by the Tamm-Dancoff method is applied to the chiral quark model. It is illustrated here by the chiral \ensuremath{\sigma} model embedded in the chiral bag environment. This simple model is used as an example and as the test for the Tamm-Dancoff inspired approximation (TDIA). Here the TDIA is employed in two ways: (i) a set of field operator equations of motion is solved between quark states and (ii) the Hamilton field operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e., hadron masses) can be found with the TDIA also. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained in the TDIA are comparable to those obtained using the usual hedgehog-based approximation. The TDIA can be used in more complex models too.

Microscopic Calculations forO(6) Nuclei by the Interacting Boson Model

We present microscopic calculations of the Interacting Boson Model (IBM) based on the shell model interaction by using the OAI mapping approach. We determine the col­ lective pairs, which correspond to the IBM bosons, by the number conserved Hartree-Fock­ Bogoluibov (HFB) and the proton-neutron Tamm-Dancoff methods, and we take into consid­ eration couplings to the non-collective degrees of freedom. The present realistic calculations are carried out for the Te, Xe and Ba isotopes. Among them, the Xe isotopes are known by numerous phenomenological works to show the 0(6) symmetry. We present the clear 0(6) symmetry in the spectra and the wave function which are microscopically obtained. Low-lying spectra of medium and medium-heavy nuclei show simple and regular structures, although these nuclei consist of many interacting protons and neutrons and their dynamics is intrinsically very complicate. This is known to be the collec­ tive motion. Especially, in the case of even-even nuclei, there are quite simpler and common features in energy levels and electro-magnetic transitions. The understand­ ing of them has been one of the main problems in nuclear structure. Many theories have been advocated, developed and extended. Among them, the Interacting Boson Model (IBM), l)- 6 ) which was first introduced by Arima and Iachello in the 1970's, has shown to be rather successful. In the IBM, nucleon collective pairs are approximated in terms of bosons. This notion can simplify the treatment of the nucleon many-body system. Furthermore this ansatz facilitates the group theoretical treatment. Originally s and d bosons, which are counterparts of S(J = 0) and D(J = 2) nucleon pairs, are introduced as the building blocks of the IBM. Because these bosons do not distinguish the proton and neutron degrees of freedom, the nucleon pair counterparts of these bosons are ambiguous. But, the s and d bosons span a U(6) space and its group chains containing the 0(3) subgroup correspond physically to vibrational, rotational and ''( unstable nuclei as limiting cases. These group chains are U(5), SU(3) and 0(6) limits. Unlike to other collective models, the IBM can give us a clear description of the 0(6) nuclei besides the U(5) and SU(3) nuclei. There are many nuclei, the spectra of which show the pattern of these group theoretical limits. Furthermore the intermediate situations between three limits are easily tractable by diagonalization of the Hamiltonian because the dimension of the original IBM space is at most about one hundred. At this stage, many phenomenological works were carried out, which showed that the low-lying states of many even-even nuclei can be explained by using six parameters of the IBM in a unified way. These parameters are considered to

A calculation of exciton energies in periodic systems with helical symmetry: Application to a hydrogen fluoride chain

AbstractAb initio Hartree–Fock crystal orbital results were used as input for the calculation of exciton energies in the Tamm–Dancoff and random‐phase approximation for polymers with helical symmetry. The calculations were applied to a hydrogen fluoride chain. We show that the Tamm–Dancoff method is a good approximation to the random‐phase theory. Furthermore, the influence of the band–band interaction in the exciton calculation has been investigated.

The electronic states of the azines. IV. Pyrazine, studied by VUV absorption, near-threshold electron energy-loss spectroscopy and ab initio multi-reference configuration interaction calculations

The present paper extends the number of known low-lying electronically excited states of pyrazine through comparison of VUV absorption and near-threshold electron energy-loss spectra. Assignments of these, and assessment of previously established states, have been carried out by all-valence electron CI studies using multi-reference multi-root approaches in a double zeta+Rydberg function basis. In general, the first members of Rydberg series are well-determined by calculation, as are the lowest ππ* and nπ* states. However, the 1B 1u/ 1B 2u states derived from the 1E 1u state in benzene are not well-calculated. It seems that the paucity of MOs of symmetry a u lies behind this and that an iterative natural orbital approach may be necessary to obtain a better fit of theory with experiment. In the assignment of cationic states, there are some differences between present large-scale CI and earlier Green function (GF) and Tamm-Dancoff (TDA) results; in particular, the CI calculations produce many more shake-up states and with a lower onset energy than the TDA method with the same basis set. One-electron properties of the pyrazine ground electronic state have also been computed, with a larger basis set.

Selection of collective degrees of freedom in the boson space

Two methods for selecting collective bosons, one proposed by Klein and Vallières and the other a number conserved Tamm-Dancoff method, are applied in this work to boson mapping methods. The first mapping to be tested is a Dyson boson mapping in the SD shell and the second is a mapping developed by Bonatsos, Klein and Li and applied to two j-shells with ¦j 1−j 2¦ = 4 . Whenever the boson mappings are accurate, the selection of collective bosons gives good results, independent of the method considered.

Spurious states in quasiparticle theory.

${0}^{+}$ spurious states arising due to the nonconservation of the number of particles, associated with the quasiparticle modified Tamm-Dancoff approximation method, up to the square of the number of particles operator are discussed. A procedure for eliminating the effects of these spurious states from the quasiparticle modified Tamm-Dancoff approximation basis states is prescribed and applied to structure studies of Ni isotopes employing the Kuo-Brown effective interaction, and the trends of the results thus obtained are compared with experiments and earlier calculations.

Electronic structures of transition-metal four-co-ordinated complexes. Part 3. Theoretical ab initio and ultraviolet photoelectron spectroscopy study of nickel(II), palladium(II), and platinum(II) bis(O,O′-diethyl dithiophosphate) square-planar complexes

The electronic structures of [Ni(dtp)2], [Pd(dtp)2], and [Pt(dtp)2][dtp = S2P(OEt)2] have been studied using pseudopotential valence-only ab initio methods, and He I and He II photoelectron spectroscopy. For [Ni(dtp)2] and [Pd(dtp)2], correlation and relaxation effects have been included in the calculation of the ionization energies by means of the extended two particle–hole Tamm–Dancoff method. The deviations from Koopmans' theorem were found to be considerably greater for the nickel than for the palladium complex. Consistent assignments of the photoelectron spectra have been proposed with the aid of these calculations.

The valence ionization energies of Ni(CN) 42- studied by X-ray emission spectroscopy and by an ab initio green's function calculation

Measurements of the Ni Lα 1.2, C Kα and N Kα emission spectra of K 2Ni(CN) 4 show that those ionized states correlating with metal 3d and ligand (1π, 5σ) ionization span an energy range of = 2 eV, in good agreement with ionization energies calculated by the extended two-particle-hole Tamm-Dancoff method.

Extension of the Tamm-Dancoff method for nuclear vibrational states

Some simple properties in the solution of the random phase approximation are discussed. By solving the problem in the Tamm-Dancoff approximation, we can obtain immediately a solution with a good accuracy for the random phase approximation together with the RPA ground state wave function. The physical picture of the correlated ground state is suggested.

Projected BCS Tamm‐Dancoff method for molecular electronic structures

AbstractA new Tamm–Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number‐projected BCS (PBCS) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one‐pair excitation terms in the Tamm‐Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin‐symmetry adapted first‐ and second‐order Tamm–Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H4 system with D2h and D4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second‐order Tamm–Dancoff correction improves the result as much as the double excitation CI. The Tamm–Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.

New Tamm-Dancoff treatment of the classical nonlinear oscillator

Heisenberg’s new Tamm-Dancoff method is applied to the 1-dimensional classical nonlinear oscillator. The procedure is seen formally to lead to an explicit solution to the initial-value problem, which is expressed in terms of infinite-dimensional matrices. The matrix transformation leading from the initial to the final data is defined by the eigenvectors and eigenvalues of the linear-eigenvalue problem. The truncation of the characteristic matrix is seen numerically to lead to a convergent approximation procedure in which the classical secular problem does not arise.