**ap**

**An International Research Journal**

**AJP**

**SSN : 0971 - 3093**

**Vol 25, No 9, September, 2016**

**25 ^{th} Anniversary Year of
AJP-2016**

**Special issue**

**on**

**Advances in High Precision Spectroscopy and
Tests of Fundamental Physics,
Part-1**

**Edited by**

**Bijaya Kumar Sahoo**

**
Asian Journal of Physics**

**(A Publication Not for
Profit)**

**
Vol. 25, No 9 (2016)**

** CONTENTS**** **

*Guest
Editorial *
* *

About the Guest Editor

Prospect of molecular clocks

*Masatoshi
Kajita *
1051

Oscillation frequencies for simultaneous trapping of heteronuclear alkali atoms

*Kiranpreet
Kaur, B K Sahoo and Bindiya
Arora *
1061

Singly charged ions for optical clocks

*N
Batra, A Roy, S Majhi, S Panja and S De
*
1069

Permanent EDM measurement in Cs using nonlinear magneto-optic rotation

*Harish
Ravi, Mangesh Bhattarai, Abhilash Y D, Ummal Momeen* and Vasant
Natarajan
*
1093

Precise many-electron calculations of isotope shift for alkali like atoms or ions

*Sourav
Roy, Anal Bhowmik and Sonjoy Majumder
*
1103

Energy level crossing of highly charged ions for optical clocks

*Yan-mei
Yu and Bing-bing
Suo *
1119

* *

The magnetic moment of the bound electron

*G
Werth and S
Sturm *
1143

Computational methods for high-precision spectroscopy of three-electron atomic systems

*Liming
Wang, Chun Li, and Zong-Chao
Yan
*
1161

Precision
measurements based on ^{40}Ca^{+} ion optical
frequency standards

*Hua
Guan, Yao Huang, Cheng-bin Li, Li-yan Tang, and Ke-lin
Gao
*
1207

Precision physics with molecules

*Amar C
Vutha
*
* *
1233

*
*

*
Asian Journal of
Physics*
Vol. 25 No 9, 2016 1051-1059

**Prospect of molecular
clocks**

Masatoshi Kajita

*National Institute of
Information and Communications Technology*

Koganei, Tokyo 184-8795, JAPAN

___________________________________________________________________________________________________________________________________

While uncertainties of some of the atomic transition frequencies
have been reduced to the level of 10^{–8}, the molecular
transition frequencies are currently diffcult to be measured with
the uncertainty below 10^{–15}. This is mainly because of
the complicated energy levels of the molecules having the
vibrational-rotational states. This paper lists some molecular
transition frequencies, which can be measured with the
uncertainties lower than 10^{–16}. © Anita Publications.
All rights reserved.

**Keywords:** Precise measurement, Cold molecules,
Molecular ion

**
Total Refs : 45**

Prospect of molecular clocks

Masatoshi Kajita

National Institute of Information and Communications Technology

Koganei, Tokyo 184-8795, JAPAN

While uncertainties of some of the atomic transition frequencies have been reduced to the level of 10–8, the molecular transition frequencies are currently difficult to be measured with the uncertainty below 10–15. This is mainly because of the complicated energy levels of the molecules having the vibrational-rotational states. This paper lists some molecular transition frequencies, which can be measured with the uncertainties lower than 10–16. © Anita Publications. All rights reserved.

Masatoshi Kajita

National Institute of Information and Communications Technology

Koganei, Tokyo 184-8795, JAPAN

While uncertainties of some of the atomic transition frequencies have been reduced to the level of 10–8, the molecular transition frequencies are currently difficult to be measured with the uncertainty below 10–15. This is mainly because of the complicated energy levels of the molecules having the vibrational-rotational states. This paper lists some molecular transition frequencies, which can be measured with the uncertainties lower than 10–16. © Anita Publications. All rights reserved.

- Prospect of molecular clocks.pdf
- Masatoshi Kajita

___________________________________________________________________________________________________________________

**
**

* Asian Journal of
Physics*
Vol. 25 No 9, 2016, 1061-1068

**Oscillation frequencies for simultaneous trapping of
heteronuclear alkali atoms**

**
**

Kiranpreet
Kaur^{a}, B K Sahoo^{b} and Bindiya
Arora^{a*}

^{
a}*Department of Physics, Guru Nanak Dev University,
Amritsar, Punjab-143 005, India*

^{
b}*Theoretical Physics Division, Physical Research
Laboratory, Navrangpura, Ahemadabad-380 009, India*

___________________________________________________________________________________________________________________________________

We investigate oscillation frequencies for simultaneous trapping of more than one type of alkali atoms in a common optical lattice. For this purpose, we present numerical results for “magic” trapping conditions, where the oscillation frequencies for two different kinds of alkali atoms using laser lights in the wavelength range 500-1200 nm are same. These wavelengths will be of immense interest for studying static and dynamic properties of boson-boson, boson-fermion, fermion-fermion, and boson-boson-boson mixtures involving different isotopes of Li, Na, K, Rb, Cs and Fr alkali atoms. In addition to this, we were also able to locate a magic wavelength around 808.1 nm where all the three Li, K, and Rb atoms are found to be suitable for oscillating at the same frequency in a common optical trap.

**Total
Refs: 53**

- Oscillation frequencies for simultaneous trapping of heteronuclear alkali atoms.pdf
- Kiranpreet Kaur, B K Sahoo and Bindiya Arora

* Asian Journal of
Physics*
Vol. 25 No 9,
2016,1069-1092

**Singly charged ions for optical clocks**

N
Batra^{1,2}, A Roy^{2}, S Majhi^{2}, S
Panja^{1,2} and S De^{1,2}

^{
1}*Academy of Scientic and Innovative Research*
(*AcSIR*)*,*

*CSIR-
National Physical Laboratory (CSIR-NPL) Campus, New Delhi,
India*

^{
2}*CSIR-National Physical Laboratory, Dr. K. S.
Krishnan Marg, New Delhi-110012, India.*

In
modern era atomic clocks are the most accurate instruments given by
the scientific community which use *State-of-the-Art*
cooling and trapping technologies. Atomic clocks at the optical
frequencies are new addition in the last one decade which provide
1s accuracy over the age of the universe. Neutral atoms in optical
lattices and single ion in a Paul trap are the two well established
techniques for optical frequency standards. In this article we
focus on the atomic ions optical frequency standards. Recent
worldwide developments, different choice of the species and
associated dominant systematics have been discussed in this review.
© Anita Publications. All rights reserved.

**
Keywords**: Atomic clocks, Frequency standards, Optical
frequency standards, Optical lattice, Ion trap, Systematic shifts,
Precision measurement.

**Total
Refs: 150**

*Asian Journal of
Physics *
Vol 25, No 9, 2016,1093-1101

**Permanent EDM measurement in Cs using nonlinear
magneto-optic rotation**

Harish Ravi, Mangesh Bhattarai, Abhilash Y D, Ummal Momeen* and Vasant Natarajan

*Department
of Physics, **Indian Institute
of Science, Bangalore-560 012, India*

**School of Advanced Sciences, VIT University, Vellore 632 014,
India*

We use the technique of chopped nonlinear magneto-optic rotation
(NMOR) at room temperature in ^{133}Cs vapor cell to
measure the permanent electric dipole moment (EDM) in the atom. The
cell has paraffin coating on the walls to increase the relaxation
time. The signature of the EDM is a shift in the Larmor precession
frequency which is correlated with the application of an E field.
We analyze errors in the technique, and show that the main source
of systematic error is the appearance of a longitudinal B field
when the E field is applied. This error can be eliminated by doing
measurements on the two ground hyperfine levels. Using an E field
of 2.6 kV/cm, we place an upper limit on the electron EDM of
2.9´10^{–22} e-cm (95% condence). This limit can be
increased by 7 orders-of-magnitude|and brought below the current
best experimental value|with easily implementable improvements to
the technique. © Anita Publications. All rights
reserved.

**Keywords**: NMOR; EDM; Paraffin coating.

**Total Refs: 14**

- Permanent EDM measurement in Cs using nonlinear magneto-optic rotation.pdf
- Harish Ravi, Mangesh Bhattarai, Abhilash Y D, Ummal Momeen and Vasant Natarajan

*Asian Journal of
Physics *
Vol 25, No 9, 2016,1103-1117

** **

**Precise many-electron calculations of isotope shift for
alkali like atoms or ions**

Sourav Roy^{1}, Anal Bhowmik^{2} and Sonjoy
Majumder^{2}

^{1}*Department of Chemistry, Ben Gurion
University of the Negev, Beer Sheva 84105, Israel*

^{2}*Department of Physics, Indian Institute
of Technology-Kharagpur, Kharagpur-721 302, India*

In this paper, we review the precise many-body calculations isotope shift for alkali and singly ionized alkaline earth atoms. Relativistic coupled cluster method is employed here to have correlation exhaustive results. We showed that the preciseness of the results not only depends on the proper consideration of excitation cluster amplitudes, but also important on exact description of Dirac-Hartree-Fock orbitals wavefunctions over the radial extent. Our results for the mass constants are also compared with the values extracted from the experimental measurements. Distinct and interesting relativistic correction of IS, magic nucleon number and even-odd staggering phenomena of nucleus are studied in terms of different isotopes. © Anita Publications. All rights reserved

**Total Refs: 62**

*Asian Journal of
Physics *
Vol 25, No 9, 2016,1119-1141

**Energy level crossing of highly charged ions for optical
clocks**

Yan-mei Yu^{1} and Bing-bing
Suo^{2}

^{1}*Beijing National Laboratory for Condensed
Matter Physics,*

*Institute of Physics, Chinese Academy of Sciences, Beijing
100190,China and*

^{2}*Institute of Modern Physics, Northwest
University, Xi’an, Shaanxi 710069*, *China*

New clock scheme based on the highly charged ions (HCIs) has been
proposed for the accuracy at 10^{–19 } recently. The
key advantage of HCIs comes from their high ionic charge. The E1
transitions in HCIs are in x-ray range usually. However, near the
level crossings, configuration crossing keeps frequencies of
transitions in the optical range and also provides wealthy chances
for looking for the relatively strong transition line for cooling.
Preliminary knowledge of energy level crossings in HCIs is very
useful to select suitable ions for better atomic clocks.. In this
paper, a large quantity of energy level data of the HCIs are
summarized in order to illustrate 3*d* − 4*s*, 4d−5s,
5d−6s, 4f −5d, 4f − 6s, 4f − 5p, and 4f − 5s crossings in
isoelectronic sequences with the increasing number of electrons.
The tendency of the energy level crossings that occur at the first
six rows of the periodic table
is reviewed. Some new HCIs near the energy level crossings are
suggested that have transitions within the wavelength range
accessible to modern lasers and have enriched sensitivity to
potential time variation of fine structure constant. © Anita
Publications. All rights reserved

**Total Refs:21**

*Asian Journal of
Physics *
Vol 25, No 9, 2016,1143-1159

** **

**The magnetic moment of the bound
electron**

G Werth^{1} and S Sturm^{2}

^{
1}*Johannes Gutenberg University, Institutfuer Physik,
55099 Mainz, Germany*

^{
2}*Max-Planck Institute for Nuclear Physics,
Saupfercheckweg, 169117 Heidelberg, Germany*

The
magnetic moments of electrons, generally expressed by the
dimensionless g-factorg =
Δ*E*/*μ*_{B}*B*Δ*m*
as scaling factor for the energy difference *ΔE* between
Zeeman levels of quantum number *m* in a magnetic field
*B* is an important quantity for our understanding of atomic
structure. Penning traps are the instruments of choice to measure
values of *g* for charged particles. We review results of
measurements performed in recent years onmulti-electron ions which
serve as test of atomic structure calculations. Very precise
results have been obtained on hydrogen- andlithium-like ions which
represent to date the most stringent test of Quantum Electrodynamic
calculations in bound systems. From a combination of experimental
and theoretical results we derived a new value for the electron's
atomic mass, improving the number listed in the tables of
fundamental constants by more than one order of magnitude.© Anita
Publications. All rights reserved.

Keywords: Magnetic moment, Spin, Zeeman levels

**Total Refs: 33**

- The magnetic moment of the bound electron.pdf
- The magnetic moment of the bound electron by G Werth and S Sturm

*Asian Journal of
Physics *
Vol 25, No 9, 2016,1161-1206

** **

**Computational methods for high-precision spectroscopy
of ****three-electron
atomic systems**

Liming Wang^{1}, Chun Li^{2}, and Zong-Chao
Yan^{3}

^{1}*Department of Physics, Henan Normal
University, Xinxiang, Henan, P. R. China 453007*

^{2}Department of Mathematics, Nanjing University,
Nanjing, Jiangsu, P. R. China 210093

^{3} Department of Physics, University of New
Brunswick, Fredericton, New Brunswick, Canada E3B
5A3

^{4}*Wuhan Institute of Physics and
Mathematics,Chinese Academy of Sciences, Wuhan, Hubei, P. R. China
430071*

Recent progress on computational methods for high precision calculations of three-electron atomic systems are reviewed. We first introduce two important methods for solving the time independent Schrödinger equation, the Rayleigh-Ritz variational method and Rayleigh-Schrödinger perturbation method. We then show how to construct a nonrelativistic wave function variationally in Hylleraas coordinates and how to solve the eigenvalue problems of the Hamiltonian for a three-electron atomic system. We then focus on computational aspects of relativistic and quantum electrodynamic corrections to atomic energy levels. Some theoretical results for nonrelativistic energy eigenvalues, ionization energies, fine structure splittings, and isotope shifts are reviewed. Finally, we include two special sections that describe, respectively, basic mathematical properties of Schrödinger operators and mathematical theory of the Fromm-Hill integral. © Anita Publications. All rights reserved.

**Keywords**: Schrödinger equation; Rayleigh-Ritz
variational method; Rayleigh-Schrödinger perturbation method;
Hamiltonian

**Total Refs:165**

*Asian Journal of
Physics *
Vol 25, No 9, 2016,1207-1231

**Precision measurements based on ^{40}Ca^{+}
ion optical frequency standards**

** **

Hua
Guan^{1, 2}, Yao Huang^{1, 2}, Cheng-bin
Li^{1}, Li-yan Tang^{1}, and Ke-lin Gao^{1,
2}*

^{
1}*State Key Laboratory of Magnetic Resonance and
Atomic and Molecular Physics, Wuhan Institute of Physics and
Mathematics,*

*Chinese
Academy of Sciences, Wuhan 430071, China*
[1]

^{
2}*Key Laboratory of Atomic Frequency Standards, Wuhan
Institute of Physics and Mathematics, Chinese Academy of Sciences,
Wuhan 430071, China*

The
development of the optical frequency standard based on trapped and
cold ^{40}Ca^{+} with the 4*s*
^{2}*S*_{1/2}–3*d*
^{2}*D*_{5/2} clock transition at 729 nm is
reported. A single ^{40}Ca^{+} ion is trapped and
laser cooled in a ring Paul trap, and the storage time for the ion
is more than one month. The linewidth of a 729 nm laser is reduced
to about 1 Hz by locking to a super cavity for longer than one
month uninterruptedly. In order to realize the frequency
comparison, two similar ^{40}Ca^{+} optical
frequency standards are established. The overall systematic
uncertainties of the clock transition of two
^{40}Ca^{+} optical frequency standards are
evaluated to be better than 6 × 10^{-17}. With an
over-one-month measurement, the frequency difference between the
two clocks is measured to be 3.2 × 10^{−17} with a
measurement uncertainty of 5.5 × 10^{−17}, considering both
the statistic (1.9 × 10^{−17}) and the systematic (5.1 ×
10^{−17}) uncertainties. By the frequency comparison in
three days uninterruptedly, a fractional stability of 7 ×
10^{−17} in 20 000 s of averaging time is achieved. At the
same time, the absolute frequency of the clock transition is
measured at 10^{-15} level by using an optical frequency
comb referenced to a Hydrogen maser which is calibrated to the SI
second through the global positioning system (GPS). The frequency
value is 411042129776401.7(1.1) Hz with the correction of the
systematic shifts. Moreover, additional two precision measurements
based on single trapped ^{40}Ca^{+} ion are carried
out. One is magic wavelengths for 4*s*
^{2}*S*_{1/2}-3*d*
^{2}*D*_{5/2} clock transition,
λ_{|mj|=1/2} = 395.7992(7) nm and λ_{|mj|=3/2} =
395.7990(7) nm are measured. It’s the first time that two magic
wavelengths for the ^{40}Ca^{+} clock-transition
are reported. And the correlation between the magic wavelengths and
the polarization direction of the linearly polarized laser is
preliminary studied. The other one is the 3*d*
^{2}*D*_{5/2} state lifetime measurement,
our result of 1174(10) ms agrees well with the experimental results
reported by P. A. Barton et al. [Phys. Rev. A 62, 032503 (2000)],
A. Kreuter et al. [Phys. Rev. A 71, 032504 (2005)] and the recent
RCC calculation result by B. K. Sahoo [Phys. Rev. A 91, 022511
(2015)].

Total
Refs : 58

*Asian Journal of
Physics
*
Vol 25, No 9 (2016) 1233-1245

**Precision physics with molecules**

Amar C Vutha

*Department
of Physics, University of Toronto, 60 St. George Street, Toronto ON
M5S 1A7, Canada*

Molecules have become an important resource for precisely measuring a number of fundamental physics quantities. This review provides an introduction to the properties of molecules that make them suitable for precision measurements, and surveys the state of the art in precision molecular physics experiments.© Anita Publications. All rights reserved.

**Keywords**:
Fundamental physics quantities; Precision measurements

**Total
Ref: 90**

___________________________________________________________________________________**________________________________________________
**

*© ANITA
PUBLICATIONS*

*All rights
reserved*