With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of ...atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the 'Förster sphere' (R < RF) this dependence transforms to the formula for electric dipole interaction energy ΔEd − d = C3/R3 and for R > RF it transforms to the formula for the van der Waals interaction energy ΔEVdW = −C6/R6. The van der Waals constant C6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J. The numerical values of the irreducible components of tensor C6 were calculated for rubidium atoms in the same Rydberg states |nlJM〉 with large quantum numbers n. We present the calculated resonance interaction energy of two rubidium atoms in the states |43D5/2M〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P3/2M〉 and of the other in the state |41F7/2M〉.
The possibilities and ways for operational tuning of optical lattice parameters, which make it possible to minimise the frequency-standard uncertainties caused by nonlinear, nondipole, and anharmonic ...effects of interaction of magnesium and calcium atoms with the optical lattice field of a magic wavelength, have been investigated.
The development of optical frequency standards with a relative uncertainty of reproducing the time and frequency units at a level as low as 10−17-10−18 calls for an unprecedented accuracy in ...estimating the role of higher orders of optical nonlinearity, caused by the influence of the optical lattice on the frequency shift of the 'clock transition'. This paper presents a systematic calculation of the contributions of multipole nonlinear anharmonic effects to the error of clocks based on optical lattices for alkaline-earth-like Sr, Yb, and Hg atoms.
Multipole, nonlinear and anharmonic effects on the optical-lattice-based clocks of Mg atoms are evaluated theoretically. Dipole polarizabilities, hyperpolarizabilities and multipolar polarizabilities ...for Mg atoms are calculated in the single-electron approximation with the use of analytical presentations for the wave and Green's functions in the modified model-potential approach. For comparison, the data are also given for atoms of the group IIb elements (Zn, Cd, Hg).
Irreducible components determining the dependence of the van der Waals coefficient C 6 ( nlJM ) on the angle θ between the interatomic and the quantisation axes of two Rb atoms in their identical ...Rydberg states nlJM 〉 are evaluated with account of the most contributing terms of the spectral resolution for the bi-atomic Green's function. Asymptotic polynomials in powers of the Rydberg-state principal quantum number n are derived for the C6 irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their n 2 S 1 2 , n 2 P 1 2,3 2 , n 2 D 3 2,5 2 and n 2 F 5 2,7 2 Rydberg states of arbitrary high n. The transformation of the van-der-Waals interaction law − C 6 R 6 into the dipole-dipole law C 3 R 3 in the case of close two-atomic states (the Förster resonance) is considered. Numerical values, the dependences on the magnetic quantum numbers M and on the angle θ of the constant C3 are determined together with the ranges of interatomic distances R, where the interaction law R − 6 transforms into the law of R − 3 .
Abstract
The increasing luminosities of future data taking at Large Hadron Collider and next generation collider experiments require an unprecedented amount of simulated events to be produced. Such ...large scale productions demand a significant amount of valuable computing resources. This brings a demand to use new approaches to event generation and simulation of detector responses. In this paper, we discuss the application of generative adversarial networks (GANs) to the simulation of the LHCb experiment events. We emphasize main pitfalls in the application of GANs and study the systematic effects in detail. The presented results are based on the Geant4 simulation of the LHCb Cherenkov detector.
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8.
Van-der-Waals interaction of atoms in dipolar Rydberg states Kamenski, Aleksandr A.; Mokhnenko, Sergey N.; Ovsiannikov, Vitaly D.
The European physical journal. D, Atomic, molecular, and optical physics,
02/2018, Volume:
72, Issue:
2
Journal Article
Peer reviewed
An asymptotic expression for the van-der-Waals constant
C
6
(
n
) ≈ –0.03
n
12
K
p
(
x
) is derived for the long-range interaction between two highly excited hydrogen atoms A and B in their extreme ...Stark states of equal principal quantum numbers
n
A
=
n
B
=
n
≫ 1 and parabolic quantum numbers
n
1(2)
=
n
- 1,
n
2(1)
=
m
= 0 in the case of collinear orientation of the Stark-state dipolar electric moments and the interatomic axis. The cubic polynomial
K
3
(
x
) in powers of reciprocal values of the principal quantum number
x
= 1/
n
and quadratic polynomial
K
2
(
y
) in powers of reciprocal values of the principal quantum number squared
y
= 1/
n
2
were determined on the basis of the standard curve fitting polynomial procedure from the calculated data for
C
6
(
n
). The transformation of attractive van-der-Waals force (
C
6
> 0) for low-energy states
n
< 23 into repulsive force (
C
6
< 0) for all higher-energy states of
n
≥ 23, is observed from the results of numerical calculations based on the second-order perturbation theory for the operator of the long-range interaction between neutral atoms. This transformation is taken into account in the asymptotic formulas (in both cases of
p
= 2, 3) by polynomials
K
p
tending to unity at
n
→
∞
(
K
p
(0) = 1). The transformation from low-
n
attractive van-der-Waals force into high-
n
repulsive force demonstrates the gradual increase of the negative contribution to
C
6
(
n
) from the lower-energy two-atomic states, of the A(B)-atom principal quantum numbers
n
′
A(B)
=
n
-Δ
n
(where Δ
n
= 1, 2, … is significantly smaller than
n
for the terms providing major contribution to the second-order series), which together with the states of
n
″
B(A)
=
n
+Δ
n
make the joint contribution proportional to
n
12
. So, the hydrogen-like manifold structure of the energy spectrum is responsible for the transformation of the power-11 asymptotic dependence
C
6
(
n
) ∝
n
11
of the low-angular-momenta Rydberg states in many-electron atoms into the power-12 dependence
C
6
(
n
) ∝
n
12
for the dipolar states of the Rydberg manifold.
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9.
van der Waals interaction of atoms in circular Rydberg states Kamenski, Aleksandr A.; Manakov, Nikolay L.; Mokhnenko, Sergey N. ...
The European physical journal. D, Atomic, molecular, and optical physics,
2018/10, Volume:
72, Issue:
10
Journal Article
Peer reviewed
Analytical expressions for the constants of resolution in powers of inverse interatomic distance 1∕
R
are determined for the energy of the long-range interaction between two atoms A and B in their ...circular Rydberg states of equal principal quantum numbers
n
A
=
n
B
≡
n
≫ 1, maximal angular momenta and magnetic quantum numbers
l
A
=
l
B
= |
m
A
| = |
m
B
| =
n
− 1 in the case of arbitrary orientation of the interatomic axis relative the axis of the
m
-quantization. Coefficients of the odd-power terms
C
k
∕
R
k
are derived for
k
= 5, 7, 9 from the first-order perturbation theory (PT) for the interaction Hamiltonian. The constant
C
6
of the van der Waals interaction Δ
E
vdW
= −
C
6
∕
R
6
, determined from the second-order PT, is resolved into irreducible components. The combinations of irreducible components determine coefficients at Legendre polynomials and/or cosine functions describing the dependence of
C
6
on the angle between the interatomic and quantization axes. The asymptotic dependence on the principal quantum number
C
6
∝
n
12
is demonstrated analytically. Polynomials in powers of
n
are derived for extrapolation of calculated data to the case of arbitrary
n
. The transformation of attractive van der Waals force (
C
6
> 0) for low-energy states
n
< 6 into repulsive force (
C
6
< 0) for all higher-energy states of
n
≥ 8 is demonstrated in numerical calculations.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Theoretical analysis is presented of the natural lifetimes and blackbody-radiation (BBR)-induced shifts and widths of Rydberg states with small and large angular momenta
l
. Asymptotic presentations ...in elementary functions are derived for matrix elements of bound-bound, bound-free and threshold radiative transitions from hydrogenic-type states with large angular momenta, applicable to both hydrogen-like and many-electron atoms and ions. For states with small angular momenta two numerical methods based on the quantum defects were used and corresponding data are compared with one another and with the most reliable data of the literature. Asymptotic approximations are derived for natural lifetimes, thermal shifts and broadening of Rydberg states of small and high
l
and principal quantum numbers
n
≫ 1.
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