Two- and three-body effective electrostatic interactions in odd configurations of the iron group

1982 ◽  
Vol 60 (9) ◽  
pp. 1223-1236
Author(s):  
C. Roth
Keyword(s):  
Electrostatic Interactions ◽  
Effective Interaction ◽  
Interaction Parameters ◽  
Iron Group ◽  
Effective Interactions ◽  
A Value ◽  
Three Body ◽  
Independent Parameters

Expressions for the two- and three-body effective interactions in the configurations l″ and l″l′ were obtained, and then specialized for the case of the odd configurations in the iron group with l having a value of 2 and l′ a value of 1.There are four independent effective interaction parameters for the configuration d″. For the configuration d″p it was shown that there are 2 independent parameters for the two-body effective interactions, and 11 independent parameters for the three-body effective interactions.The results are being utilized in general investigtions for the odd configurations (3d + 4s)″4p in the iron group, and subsequently for the odd configurations in the palladium and platinum groups.

A new combining rule for fluid mixtures

2009 ◽  
Vol 74 (2) ◽  
pp. 363-391 ◽  
Author(s):  
José Alfredo González-Calderón ◽  
Fernando del Río
Keyword(s):  
Experimental Data ◽  
Small Molecules ◽  
Binary Mixtures ◽  
Electrostatic Interactions ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Interaction Parameters ◽  
Effective Interactions ◽  
Fluid Mixtures ◽  
The Cross

We present evidence for the regular behaviour of the Boyle temperature TB in gaseous binary mixtures of small molecules with negligible multipolar moments. We use this regularity to construct a new combining rule for the prediction of the cross interaction u12(r) in those mixtures. The combining rule gives TB of the cross interaction as the harmonic mean of the Boyle temperatures of the pure components. The validity of this harmonic rule is based on experimental data of 28 binary mixtures, whose TB have been obtained from experimental data of the cross virial coefficient B12(T). In determining TB we make use of non-conformal potentials that have been proven to represent very accurately the effective interactions of the molecules investigated. The new combining rule is used to give interaction parameters of several dozens of binary mixtures involving noble gases (Ne, Ar, Kr and Xe), diatomic molecules (N2, O2 and CO) and n-alkanes (from methane to n-octane). These interaction parameters lead to a prediction of cross virial coefficients B12(T) within experimental error. Electrostatic interactions, originating in permanent dipolar, quadrupolar, octupolar and hexadecapolar moments and exemplified by molecules of HCl, CO2, CF4 and SF6, depart from the regular non-polar behaviour.

scholarly journals Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Eric D’Hoker ◽  
Carlos R. Mafra ◽  
Boris Pioline ◽  
Oliver Schlotterer
Keyword(s):  
Moduli Space ◽  
Effective Interaction ◽  
Type Ii ◽  
Leading Order ◽  
Effective Interactions ◽  
Heterotic String Theory ◽  
Genus Two ◽  
Genus One ◽  
Graph Function ◽  
Point Amplitude

Abstract In an earlier paper, we constructed the genus-two amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1)R-preserving amplitudes such as for five gravitons, and for U(1)R-violating amplitudes such as for one dilaton and four gravitons. At each order in α′, the coefficients of the effective interactions are given by integrals over moduli space of genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading orders, the coefficients of the effective interactions D2ℛ5 and D4ℛ5 are found to match those of D4ℛ4 and D6ℛ4, respectively, as required by non-linear supersymmetry. To the next order, a D6ℛ5 effective interaction arises, which is independent of the supersymmetric completion of D8ℛ4, and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order D6ℛ5, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)R-violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.

THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

2005 ◽  
Vol 19 (30) ◽  
pp. 1793-1802 ◽  
Author(s):  
M. MODARRES
Keyword(s):  
Angular Momentum ◽  
Ground State Energy ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Interatomic Potentials ◽  
Channel Correlation ◽  
P Waves ◽  
Effective Interactions ◽  
Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

scholarly journals FORMAL RELATION AMONG VARIOUS HERMITIAN AND NON-HERMITIAN EFFECTIVE INTERACTIONS

2005 ◽  
Vol 14 (01) ◽  
pp. 21-28 ◽  
Author(s):  
RYOJI OKAMOTO ◽  
SHINICHIRO FUJII ◽  
KENJI SUZUKI
Keyword(s):  
Effective Interaction ◽  
Model Space ◽  
General Definition ◽  
Effective Interactions ◽  
Formal Relation ◽  
Definition Of ◽  
Effective Hamiltonians

A general definition of the model-space effective interaction is given. The energy-independent effective Hamiltonians derived in a time-independent way are classified systematically.

Volume transition effects on the correlations and effective interactions among highly charged microgels

Soft Matter ◽  
2020 ◽  
Vol 16 (21) ◽  
pp. 5081-5093 ◽  
Author(s):  
L. A. Aguirre-Manzo ◽  
P. González-Mozuelos
Keyword(s):  
Effective Interaction ◽  
Counterion Condensation ◽  
Effective Interactions ◽  
Volume Transition ◽  
Transition Effects

Microgels shrinkage promotes counterion condensation, which in the highly charged regime markedly inhibits the effective interaction and induces strong counterion–counterion correlations that deviate this potential from the traditional Yukawa shape.

scholarly journals Effective interactions for the three-body problem

2004 ◽  
Vol 70 (1) ◽  
Author(s):  
T. C. Luu ◽  
S. Bogner ◽  
W. C. Haxton ◽  
P. Navrátil
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Effective Interactions ◽  
Three Body

scholarly journals Ion-specific thermodynamical properties of aqueous proteins

2010 ◽  
Vol 82 (1) ◽  
pp. 109-126 ◽  
Author(s):  
Eduardo R.A. Lima ◽  
Evaristo C. Biscaia Jr. ◽  
Mathias Boström ◽  
Frederico W. Tavares
Keyword(s):  
Electrostatic Interactions ◽  
Colloidal Particles ◽  
Effective Interaction ◽  
Virial Coefficients ◽  
Water Structure ◽  
Hydrophobic Surface ◽  
Colloidal Systems ◽  
Salt Solutions ◽  
Monovalent Ions ◽  
Pharmaceutical Industries

Ion-specific interactions between two colloidal particles are calculated using a modified Poisson-Boltzmann (PB)equationandMonteCarlo(MC)simulations. PBequationspresentgoodresultsofionicconcentration profiles around a macroion, especially for salt solutions containing monovalent ions. These equations include not only electrostatic interactions, but also dispersion potentials originated from polarizabilities of ions and proteins. This enables us to predict ion-specific properties of colloidal systems. We compared results obtained from the modified PB equation with those from MC simulations and integral equations. Phase diagrams and osmotic second virial coefficients are also presented for different salt solutions at different pH and ionic strengths, in agreement with the experimental results observed Hofmeister effects. In order to include the water structure and hydration effect, we have used an effective interaction obtained from molecular dynamics of each ion and a hydrophobic surface combined with PB equation. The method has been proved to be efficient and suitable for describing phenomena where the water structure close to the interface plays an essential role. Important thermodynamic properties related to protein aggregation, essential in biotechnology and pharmaceutical industries, can be obtained from the method shown here.

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