Hyperfine structure measurements over long chains of one element
isotopes by means of laser spectroscopy in atomic beam apparatus
A. Kopystyńska1, S. Chojnacki2,3, A. Gluzicka1, J. Kownacki3
and T. T. Inamura4,3
1
Institute of Experimental Physics, Warsaw University, 2Świętokrzyska Academy, Kielce, 3Heavy Ion Laboratory, Warsaw University and 4RIKEN and JST, Japan
1. Introduction
The hyperfine structure of spectroscopic lines reflects the electromagnetic interaction between nucleus and its outer electrons. Measurements of these structures lead to
the direct and model independent information about the nucleus. The Hamiltonian describing hyperfine structure of an atomic level is



    

3( I J ) 2  23 I J  ( I I )( JJ )
,
H  AhI J  Bh
2 I (2 I  1) J (2 J  1)
where A and B are the magnetic dipole and electric quadrupole coupling constants, h is
the Planck’s constant, I is the nuclear spin and J is the total electronic angular momentum of the atom in particular state. The eigenstates of the Hamiltonian are labelled by
the total angular momentum F = J + I and have eigenenergy
E F  12 AhK  Bh
3K ( K  1)  4 I ( I  1) J ( J  1)
,
8I (2 I  1) J (2 J  1)
where K = F(F + 1) – I(I + 1) – J(J +1). The electronic quadrupole interaction is present only in case of I, J  1. The A and B constants are given by

 I B ( 0)
A  
and B  eQs zz (0)
IJ
where μI denotes nuclear magnetic dipole moment, B (0) – an average magnetic field
induced by outer electrons in the place of nucleus, eQs – spectroscopic nuclear electric
quadrupole moment and φzz(0) is an average gradient of electric field in z direction induced by outer electrons in the place of nucleus.
In order to find the nuclear magnetic dipole moment μI or gI factor, a ratio of the
A constants should be obtained for the same atomic fine structure state of different isotopes, as for example in the case of
23
Na and
1
24
Na, where A(24,2S1/2)/ A(23,2S1/2) =
gI(24)/gI(23). This relation is true only in the case, when the nucleus is considered as a
point charge and if one of the gI = μI/I factors is known with enough high precision.
This same may be done for the hyperfine B constants. In our example it is B(24)/B(23) =
Qs(24)/Qs(23). In the case of strong coupling, corresponding to the strong deformation,
the relation between the spectroscopic nuclear quadrupole moment Qs and the intrinsic
nuclear quadrupole moment Q0 is Qs  Q0 I (2I  1) /( I  1)(2 I  3) .
The isotope shift originates from two phenomena: the mass shift and the volume
(or field) shift. The optical isotope shift between two isotopes with mass numbers A1
, A2
1 , A2
and A2, observed in the transition i, can be written as  A1 , A2   iA,mass
, where
  iA, 1field
 A2  A1 
 with M i  M i ,normal  M i , specific , i.e. normal mass shift plus speA
A
 1 2 
,A
 iA,mass
 Mi 
1
2
cific mass shift. The field shift is due to the variation in nuclear charge distribution
among different isotopes of the same element. The variation may be caused by changes
in the volume or shape of the charge distribution. The field shift can be written as
,A
 iA, field
 Fi  r 2
1
2
A1 , A2
, where Fi is a spectroscopic constant, specific for the element and
the transition.
If the nucleus is represented by a point charge, the electronic wavefunction depends only on the nuclear charge and for different isotopes of the same element is the
same. Then the ratio between the dipole interaction constants of two isotopes is equal to
the ratio of their gyromagnetic nuclear factors, as it was mentioned above. Owing to the
finite size of the nucleus this relation is not exactly satisfied by the experimental results.
As a measure of the finite size influence on the dipole constants of isotopes 1 and 2 the
hyperfine anomaly has been introduced in the form 12  ( A1 / A2 )( g I2 / g 1I )  1, where
A1,2 are the dipole interaction constants and gI are the adequate nuclear g factors. There
are two corrections: one introduced by Rosenthal and Breit, and the other introduced by
Bohr and Weisskopf. The latter is due to the distribution of the magnetisation inside the
finite volume of nucleus and is much larger than the former one.
2. Long range program
The main scope of the research planned in our laboratory is to measure the atomic hyperfine splitting (hfs) and the isotope shifts (IS) over a long chain of isotopes for
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the given element. The elements of interest are sodium and some lanthanides, such as
Eu, Nd and Gd. Even though some isotopes of these elements were studied [1-3], the
systematic data are still needed. From the obtained experimental data the hyperfine
structure constants A and B can be calculated and then the determination of such the
nuclear properties as magnetic dipole and electric quadrupole moments is possible.
Moreover, from the data on IS a change in the mean square charge radius  r 2
A, A '
can
be deduced. After some modification of the apparatus, which we plan in the future, also
the magnetic hyperfine anomaly could be measured. All the above mentioned information about the nuclear properties for long chains of isotopes are of great value for nuclear physics, because in such experiments they are obtained by model independent
means.
The atomic spectroscopic techniques give the possibility to study the hyperfine
interactions between the nucleus and its outer electrons. Laser-induced fluorescence
spectroscopy applied to a thermal atomic beam is one of the best methods for studying
the hfs and IS, because it is Doppler free to first order. If there is also the possibility of
using a double resonance technique with its still higher accuracy, the obtained results
permit to determine the hyperfine anomaly 12 as well.
Due to the fact that there are no systematic data on long chains of many elements
we would like to perform such a research with our high-resolution laser spectrometer.
We plan also to make use of the double resonance technique and in this way to improve
the accuracy of measurements of 100 – 1000 times. In such a method the transition between chosen Zeeman sublevels with different populations obtained through the optical
pumping is induced by a radiofrequency magnetic field. Due to the high accuracy of
these kind measurements (the linewidth is of the order of tens kHz) it is possible to estimate also the hyperfine anomaly. With such a modification of our atomic beam apparatus we will have equipment that now is rather unique in the world.
3. Present state of research
At the present the hfs of the 3 2 P3 / 2 state of sodium radioactive isotopes with
atomic masses 22 and 24 as well as their isotope shifts with respect to the natural isotope 23Na are studied. Of the special interest is the isotope 24Na because there are no ex-
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perimental data on its electric quadrupole moment, but some calculations indicate that it
is rather large [4].
The measurements are done with a laser spectrometer [5], which consists of the
following systems.
1. The atomic beam apparatus is shown in Fig.1. The beam of sodium atoms is produced in an oven, where a molybdenum crucible containing the sample is placed.
The crucible is heated by thermoelectron bombardment. The thermoelectrons are
emitted from a wire and accelerated by 0.5 – 1 kV potential difference between the
wire and the crucible. The wire current intensity is about 100 A. An adjustable slit
defines the atomic beam divergence; the spherical mirror and two glass lenses collect fluorescence photons onto the entrance hole of a diaphragm placed in front of
the photomultiplier. In order to reduce the background due to the scattered light in
the arm introducing the laser beam into atomic beam apparatus 3 iris diaphragms
(Fig. 2) are placed.
Fig. 1. (a) Atomic beam apparatus cut in the plane of laser and atomic beams; (b) cut
in the perpendicular plane. 1. Oven housing, 2. Crucible, 3. Graphite diaphragm,
4. Adjustable slit, 5. Spherical mirror, 6. Photomultiplier, 7. Brewster window,
8. Iris diaphragms, 9. Valve, 10. Wood’s horn.
2. The laser system consists of a c.w. ring dye laser with Rhodamine 6G pumped with
the green line (514.5 nm) of an argon ion laser (25 W in all lines). In a single mode
operation the output power of the dye laser is about 400 mW and the linewidth is
about 1 MHz. Intensity of the laser beam interacting with atoms is attenuated to less
4
than 1 mW by means of density filters. Laser light frequency is electronically tuned
to the resonance and scanned through the hyperfine components of the atomic transitions of interest. The wavelength of the laser light is measured by a wavemeter
with an accuracy of 0.001 nm.
3. The data acquisition system consists of the photomultiplier (EMI 9635QB) operating in a single-photon counting mode, a fast amplifier–discriminator and IBM PC
compatible computer with a program simulating multichannel analyser. The Fabry –
Pèrot confocal interferometer with FSR of 150 MHz and finesse about 80 is used to
calibrate the laser scans.
Fig. 2. Diaphragm set-up. Micrometer screws allow changing position and diameter
of the iris diaphragm. 1. Iris diaphragm, 2. Micrometer screw, 3. Horizontal guide
bars, 4. Vertical guide bars, 5. 6. and 7. Springs, 8. Seals.
4. Appendix
Short history of the organisation and work of the Laboratory of Laser Spectroscopy
of Radioactive Nuclei has tree stages:
1. In 1995 the Laboratory was organised starting from the very beginning. It was constructed inside of the HIL building and equipped in the fundamental apparatus:
atomic beam and lasers. The existence and work of the laboratory was presented for
the first time during an International Workshop on Application of Lasers in Atomic
5
Nuclei Research, Poznań (February 1997). In the stage of starting of the laboratory
the following persons were involved:
A. Kopystyńska and M. Kraińska-Miszczak, Institute of Experimental Physics,
Warsaw University,
J. Kownacki, E. Wesołowski and technical staff of HIL, Warsaw University,
S. Chojnacki, Świętokrzyska Academy, Kielce,
S. G. Zemlanoy, JINR, Dubna, Russia (few visits of short duration)
2. In 1997 we started to measure the hyperfine structure of 32P3/2 state of 23Na in order
to estimate the accuracy and sensitivity of our experimental system, which we call
High Resolution Laser Spectrometer. In order to measure the isotope shift and other
nuclear properties we prepared the apparatus to work with radioactive sodium isotopes (22Na and 24Na) produced in the cyclotron. The staff involved in this stage of
work was following.
A. Kopystyńska, A. Gluzicka (Ph.D. student since 2000) and 3 students preparing
their Master Thesis, Institute of Experimental Physics, Warsaw University,
J. Kownacki and technical staff of HIL, Warsaw University,
S. Chojnacki, Świętokrzyska Academy, Kielce,
T. T. Inamura, RIKEN and JST, Japan (May 1998 – April 2001),
S. G. Zemlanoy, JINR, Dubna, Russia (one month in 2000).
H. Szlęzak (Ph.D. student since June 2001)
3. Now we plan to complete the study of radioactive sodium isotopes
22
Na and
24
Na
and switch to the rare-earth elements. We also plan to modify our apparatus and in
this way to improve its accuracy significantly. Then we will measure the hyperfine
magnetic anomaly too.
References
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2.
3.
4.
W. Pietsch, G.H. Guthöhrlein, H. Jäger, L. Windholz, Z.Phys. D21,189(1991)
W.J. Childs, Phys.Rev. A44,760(1991)
S.B. Dutta, A.G. Martin, W.F. Rogers, D.L.Clark, Phys.Rev. C42,1911(1990)
M. Keim, U. Georg, A. Klein, R. Neugart, M. Neuroth, S. Wilbert, P. Lievens, L.
Vermeeren, B.A. Brown and the ISOLDE Collaboration, Eur.Phys.J. A8,31(2000)
5. Kopystyńska, S. Chojnacki, T.T. Inamura, M. Kisieliński, M. Kowalczyk, E.
Kulczycka, E. Wesołowski and S.G. Zemlyanoi, Proceedings of the International
Conference on Application of Lasers in Atomic Nuclei Research, Poznań – 1999,
p.121, Dubna 2000.
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