A hydrogen atom in a uniform electric field

Damburg, R J; Колосов, В. В.

doi:10.1088/0022-3700/9/18/006

Cited by 173 publications

(69 citation statements)

References 13 publications

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“…In addition, it should be noticed that the inaccuracies at excessively large field of [9] have been pointed out by the same authors in [27]. However, not all atomic states considered in [9] were treated in the later investigation [27]. Our data for the ground state indicated in Table I are consistent with the numerical results obtained in [27].…”

Section: Numerical Calculationssupporting

confidence: 87%

“…which yields very accurate data for all experimentally accessible electric field strengths to date. In addition, it should be noticed that the inaccuracies at excessively large field of [9] have been pointed out by the same authors in [27]. However, not all atomic states considered in [9] were treated in the later investigation [27].…”

Section: Numerical Calculationsmentioning

confidence: 93%

“…(9), (13)(14)(15), (28)(29)(30)(31)(32)(33), (59)(60)(61)(62)(63)(64)(65)(66)(67) and (73) in [1]. The atomic unit system is used in the sequel, as is customary for this type of calculation [1,6,9,11]. The unit of energy is α 2 m e c 2 = 27.211 eV where α is the fine structure constant, and the unit of the electric field is the field strength felt by an electron at a distance of one Bohr radius a Bohr to a nucleus of elementary charge, which is 1/(4 π ǫ 0 ) (e/a 2 Bohr ) = 5.142 × 10 3 MV/cm (here, ǫ 0 is the permittivity of the vacuum).…”

Section: Numerical Calculationsmentioning

confidence: 99%

“…Results are compared to the numerical calculation [9]. which yields very accurate data for all experimentally accessible electric field strengths to date.…”

Section: Numerical Calculationsmentioning

confidence: 99%

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Resummation of the divergent perturbation series for a hydrogen atom in an electric field

Jentschura

2001

Phys. Rev. A

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We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Padé resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. 317, 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Padé approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.11.15. Bt, 11.10.Jj, 32.60.+i, 32.70.Jz

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Section: Numerical Calculationssupporting

confidence: 87%

Section: Numerical Calculationsmentioning

confidence: 93%

Section: Numerical Calculationsmentioning

confidence: 99%

“…Results are compared to the numerical calculation [9]. which yields very accurate data for all experimentally accessible electric field strengths to date.…”

Section: Numerical Calculationsmentioning

confidence: 99%

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Resummation of the divergent perturbation series for a hydrogen atom in an electric field

Jentschura

2001

Phys. Rev. A

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“…The coefficients are real, not complex [18]. An established method for the determination of the width is by numerical diagonalization of the Hamiltonian matrix [19][20][21]. It is argued here that the full complex energy eigenvalue, including the width, can also be inferred from the divergent perturbation series by the resummation method defined in Eqs.…”

mentioning

confidence: 99%

Resummation of nonalternating divergent perturbative expansions

Jentschura

2000

Phys. Rev. D

167

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A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Padé method. Of crucial importance is a special integration contour in the complex plane. Nonperturbative imaginary contributions can be inferred from the purely real perturbative coefficients. A connection is drawn from the quantum field theoretic problem of resummation to divergent perturbative expansions in other areas of physics.PACS numbers: 11.15. Bt, 11.10.Jj, 12.20.Ds, 11.25.Sq In view of the probable divergence of quantum field theory in higher order [1,2], the resummation of the perturbation series is necessary for obtaining finite answers to physical problems. While the divergent expansions probably constitute asymptotic series [3], it is unclear whether unique answers can be inferred from perturbation theory [4,5]. Significant problems in the resummation are caused by infrared (IR) renormalons. These are contributions corresponding to nonalternating divergent perturbation series. The IR renormalons are responsible for the Borel-nonsummability of a number of field theories including quantum chromodynamics (QCD) and quantum electrodynamics (QED) [4,6].Here I advocate a modification of the resummation method proposed in [5,7] for nonalternating divergent perturbation series. The method starts with a given input series,

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Effect of thin space‐charge layers on exciton reflectance

Киселев

Novikov²,

Cherednichenko³

et al. 1986

Physica Status Solidi (b)

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Resonance reflectance in semiconductors in the frequency region of exciton transitions depends strongly on characteristics of the near-surface space-charge layers. It is shown by numerical computation that the majority of the exciton reflection lineshapes observed on CdS earlier may be explained by the presence of a thin (10 to 100 nm) space-charge layer with a relatively high (104 to lo5 V/cm) surface electric field. Various treatments of surfaces alter charges on and below them thus modifying the electric field distribution. The latter causes changes in the exciton reflectance. Transformations of the exciton lineshapes under the action of illumination and electron bombardment are discussed in detail for the case of CdS. The lineshapes show drastic variations with expositions of both influences. In a single experiment one may observe all of the anomalies typical for the thin space-charge layers. KO34@HUHeHT OTpameHHR CBeTa B 06naCT1.I 3HCEITOHHbIX IlepeXOHOB IIOJIyIIPOBOL(HMIC0B CHJIbHO 3aBHCHT OT COCTOFIHHR rlOBepXHOCTH 1.I IIpHIlOBepXHOCTHOrO CJIOR. YMCJIeHHbIfi PaCqeT rIOICa3bIBaeT, 9 T O 6OJlbJJIHHCTBO HOHTYPOB 3KCHTOHHOrO OTpameHHR, Ha6JIH)AaB-LUHXCH paHW Ha CdS, MOrYT 6bITb 063RCHeHbI IIpHCYTCTBMeM TOHKOI' O, OT 10 L(0 100 nm, CJlOR IlpOCTpaHCTBeHHOrO 3apRAa CO CpaBHMTeJIbHO BbICOICHM, OT lo4 HO 10' V/Cm, 3HaYeIIHeM HaIIPFI)f(eHHOCTM IIOBePXHOCTHOrO 3JIeKTPH9eCKOrO nOJIFI. Pa3JIMYHbIe B03-HefiCTBHR Ha IIOBepXHOCTb H3MeHRH)T IlOBepXHOCTHbIfi H npOCTpaHCTBeHHbIfi 3aPRHb1, €i EI3MeHeHHH) 3KCMTOHHOrO OTpaWeHHR CBeTa. n o n p o 6~0 PaCCMOTpeHa IIepeCTpOfiHa KOHTypa OTpaXeHHR B CdS npEi ZefiCTBHEI 3aCBeTHM M 3JleIcTpOIIHO~ 60M6apAHpOBJSM. Ha6~110~(an~cb CHJIbHbIe H3MeHeHHR KOHTYpa C POCTOM 3 K C I I 0 3 H 4 H M IIpH060Mx B03AefiCT-BHRX. B OAHOM 3IrCnepHMeHTe MOECHO IIOJIyWlTb BCe OCO6eHHOCTII 3KCHTOHHOrO OTpa-H~M~H R I R oaHospeMeHHo pacnpeAeneHxe ~J I~K T P M~I~C H O~O n o m . IlocneaHee 1.1 npmomrT meiiiiR xapaKTepHbie n n~ TOHKXX moeB npocTpaHcTseHHoro a a p~~a .

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A hydrogen atom in a uniform electric field

Cited by 173 publications

References 13 publications

Resummation of the divergent perturbation series for a hydrogen atom in an electric field

Resummation of the divergent perturbation series for a hydrogen atom in an electric field

Resummation of nonalternating divergent perturbative expansions

Effect of thin space‐charge layers on exciton reflectance

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