- Email: [email protected]
X-ray spectra from laser produced highly ionized hafnium plasma in the 4.1–4.5 Å range
8 January 1996
PHYSICS
ELSEVIER
Physics Letters A 210 (1996)
LETTERS
A
195-197
X-ray spectra from laser produced highly ionized hafnium plasma in the 4.1-4.5 A range Chenzhong ’
Department
Dong a, Yuqing Zhou b, Baohang Zhang b
of Physics, Northwest
b Sauthwesr Institute
of Nuclear
Normal
University,
Physics and Chemistry,
Received 8 May 1995; revised manuscript received
13September
Lanzhou
730070,
China
Chengdu
610003,
China
1995; accepted for publication 2 November
1995
Communicated by B. Fricke
Abstract X-ray spectra of highly ionized hafnium atoms have been obtained from laser produced plasmas in the 4.1-4.5 A range. Using quasi-relativistic configuration interaction calculations of the wavelengths and transition probabilities, the observed spectral band structure can be interpreted as being due to 3d-6f transitions of the NiI-GeI like ionization states of hafnium. Keywords:
X-ray spectra; Band structure; Quasi-relativistic
The X-ray spectrum ments
is of great
of highly
interest
ionized
in plasma
heavy
diagnostic
configuration; Interaction theory
elestud-
ies in inertial confinement fusion experiments and Xray laser studies [ 1,2]. Recently, many X-ray spectra of heavy elements have been identified as belonging to the isoelectronic sequence of NiI and neighbouring ionization states [ 3-101. Investigations for highly ionized hafnium atoms have been carried out for 3d4p transitions in the 7.0-8.0 A range [ 3,9], for 3d-4f transitions in the 6.1-6.6 A range [ 7,9] and for 3d-Sf transitions in the 4.6-5.0 8, range [ lo]. In the present Letter, we report an extended analysis of X-ray band spectra of highly ionized hafnium atoms from laser produced plasmas in the 4.1-4.5 A range. The experiments were performed at the Xing-Guang laser facility at the Institute of Nuclear Physics and Chemistry of the Chinese Academic of Engineering Physics (CAEP) . The beam of the frequency-doubled 0.53 pm Nd-glass laser was focused onto a solid planar target. The pulse length was 800 ps and the aver-
037%9601/96/$12.00
@
SSD/O375-9601(95)00901-9
age laser flux was lOI W/cm2. The emission spectra in the 4.1-4.5 8, range were observed by a PET ( 2d = 8.742 A) flat crystal spectrometer and recorded on Kodak AA5 film. The experimental spectra are shown in Fig. 1, the measured mean wavelengths and their full widths at half maxium (FWHM) of all peaks are given in Table 1. The uncertainties of the measured wavelengths are within f0.003 A in the experiments. More details are given in Ref. [ 91. In the present Letter, calculations of wavelengths and transition probabilities are made out using Cowan’s code [ 111 including configuration interaction and relativistic corrections. Our calculations show that the observed spectra are due to 3d-6f transitions of NiI and low ionized states CuI-GeI of the hafnium atom. As the differences between the binding energies of the 4s, 4p, 4d etc. electrons are small compared to the plasma temperature, many possible transition arrays have been considered in the calculations. It is found that the transition lines belonging to
I996 Elsevier Science B.V. All rights reserved
C. Dong et al./ Physics Letters A 210 (19%) 195-197
196
Ij(A)
=C1c(l\i)exp(-41n{2[(A-Ai)/S]2}) i
X
exp(
-fiE;/KT,),
(1)
where 10( Ai) is the theoretical transition probability at wavelength Ai, K is the Boltzmann constant, AE; is the energy spread of the upper configuration, and T, is the temperature of the electrons of the plasma. The summation is performed only for overlapping lines having large transition probabilities. Under the high temperature condition, AEi < KT,, the Boltzmann factor exp( -A,!$/KT,) tends to unity. Considering the overlapping of the different ionization state spectra, the intensity of the theoretical spectrum is calculated as I(A)
I
4.1
I
I
4.2
4.3
Wavelength Fig.
1.Experimental
4.4
4.5
( W)
spectrum (solid line) and theoretical spectrum
(dashed line) of highly ionized hafnium atoms in the 4.1-4.5
%,
wavelength range. The numbers correspond to the labels in Table
the different ionization states are separated, but those of the same ionization state are nearly superimposed and not distinguishable from one another according to directly calculated data for individual lines, except for two strong lines of the 3d”-3d96f transition of the Ni-like ionization state which involved only one single 3d inner-shell electron excitation. In order to interpret the band structure features of the observed spectra, we consider the broadening of the individual lines and overlapping of a large number of transition lines in the ionization states. We assumed for each broadened line a Gaussian shape and a FWHM of S, in the local thermodynamic equilibrium approximation. The intensity of the overlapping spectra from a single ionization state j is given by
= C j
wjlj(A),
(2)
where the summation over j includes the possible ionization states in the plasma, wj is the weight factor of ionization state j, which can be estimated simply by comparing the intensity ratio of the theoretical peak with the experimental one. In the detailed calculations, the experimental widths (0.008 A) of the isolated 3ds/*-6fs,2 and 3d5/2-6f7,2 transitions of the Ni-like ion were used as S in Eqs. ( 1) and (2). In the case of the Cu-like ion, we calculate the 3d-6f transitions in the presence of a single 41 “spectator” electron (1 = s, p and d). For the Zn-like ion, we consider the spectator electron configurations 4s4p, 4s4d and 4p2. The 4s24p, 4s4p2 and 4p” spectators are included for the Ga-like calculation. The 4s24p2 spectator is considered in the calculation of the Ge-like spectrum. The comparison of our calculation results with experimental spectra is given in Fig. 1, where the weight factors Wj for the NiI-GeI ionization states are 1.0, 0.25,O. 10,0.07 and 0.04, respectively. The calculated mean wavelengths and the FWHMs of the band peaks are given in Table 1. It can be seen from Fig. 1 that the structure features of the observed spectra are in good agreement with the ab initio calculations. The differences between the computed mean wavelengths and observed ones, about 0.007 A, may be mainly due to some weak configuration interactions and residual relativistic effects which have not been included in the present calculations. In addition, the contributions of a large number of weak
C. Dong et al./Physics Table I The mean wavelengths Label
2 3 4 5 6 7 8 9 IO
Ion
Letters A 210 (1996) 195-197
and full width at half maxium of the peaks produced
197
by highly ionized hafnium
atoms in the 4.1-4.5
8, range
Transition
NiI Cul Nil ZnI
4.1 16 4.177 4.197 4.238
Cul Gal
4.257 4.295
Znl Gel Gal Gel
4.317 4.358 4.380 4.441
lines (their weight transition probabilities being less than 1 .O x 1014 SK’ ) have been neglected in the present synthetic spectrum. In conclusion, the X-ray spectra from a laser produced highly ionized hafnium plasma in the 4.1-4.5 A range have been obtained and identified as 3d-6f transitions from Ni-like to Ge-like ionization states. It is found that the traditional theoretical method used in the present analysis is still valid to interpret these complex spectra. In order to illustrate the validity, we have also carried out a similar calculation for highly ionized gold atoms. Our new results are in good agreement with the previous theoretical ones [5] of the spin-orbit splitting array (SOSA) model [ 121. An isoelectronic comparison shows that the structure features of the 3d-6f spectra of highly ionized hafnium atoms are similar to those of other high-Z elements reported in Refs. [ 5,681. Peaks corresponding to different ionization states are found to be well separated. They can therefore serve as an excellent means for the determination of ionization states of highly ionized heavy atoms. This work was supported by the Foundation of the Chinese Academy of Engineering Physics and the Natural Science Foundation of Gansu Province.
4.1 I1 4.169 4.190 4.228 4.25 I 4.294 4.3 I I 4.352 4.380 4.440
0.008 0.01 I 0.008 0.014 0.012 0.010 0.010 0.012 0.01 I 0.014
0.008 0.010 0.008 0.010 0.010 0.01 I
0.010 0.010 0.012 0.012
References [ 1] D. Mathews, in: Proc. 8th Int. Coil. on Ultraviolet and Xray spectroscopy of astrophysical and laboratory plasmas (Washington, DC, 1984). [2] S. Maxon, P Hagelstein, K. Read and J. Scofield, J. AppI. Phys. 57 (1985) 1706. [3] P. Mandelbaum and M. Klapisch, A. Bar-Shalom and J.-L. Schwab, Phys. Ser. 27 (1983) 39. [4] P. Audebert, J.-C. Gauthier, J.-I? Geindre, C. ChenaisPopovics, C. Bauche-Amoult, J.C. Bauche and M. Klapisch, Phys. Rev. A 32 (1985) 409. [5] A. Zigler, M. Klapisch and I? Mandelbaum, Phys. L&t. A I I7 (1986) 31. [6] C. Bauche-Amoult, E. Luc-Koenig, J.-F. Wyart, J.-P. Geindre, P, Audebcrt, I? Monier, J.-C. Gauthier and C. ChenaisPopovics, Phys. Rev. A 33 ( 1986) 791. [7] M. Klapisch, I? Mandelbaum, A. Zigler, C. Bauche-Amoult and J. Bauche, Phys. Ser. 34 ( 1986) 5 I. [S] N. Tragin, J.-P. Geindre, P Monier, J.-C. Gauthier, C. Chenais-Popovics, J.-F. Wyart and C. Bauche-Amoult, Phys. Ser. 37 ( 1988) 72. [9] Y.-Q. Zhou, B.-H. Zhang, G.-H. Yang, A.-L. Lci and C.-Z. Dong, Acta Phys. Sin. 43 ( 1994) 1624. [ IO] C.-Z. Dong, Y.-Q. Zhou and B.-H. Zhang, J. Phys. B ( 1995), to be published. [I I ] R.D. Cowan, The theory of atomic structure and spectra (University of California Press, Berkeley, I98 I ). [ 121 C. Bauche-Smoult, J. Bauche and M. Klapisch, Phys. Rev. A 31 (1985) 2248.
PHYSICS
ELSEVIER
Physics Letters A 210 (1996)
LETTERS
A
195-197
X-ray spectra from laser produced highly ionized hafnium plasma in the 4.1-4.5 A range Chenzhong ’
Department
Dong a, Yuqing Zhou b, Baohang Zhang b
of Physics, Northwest
b Sauthwesr Institute
of Nuclear
Normal
University,
Physics and Chemistry,
Received 8 May 1995; revised manuscript received
13September
Lanzhou
730070,
China
Chengdu
610003,
China
1995; accepted for publication 2 November
1995
Communicated by B. Fricke
Abstract X-ray spectra of highly ionized hafnium atoms have been obtained from laser produced plasmas in the 4.1-4.5 A range. Using quasi-relativistic configuration interaction calculations of the wavelengths and transition probabilities, the observed spectral band structure can be interpreted as being due to 3d-6f transitions of the NiI-GeI like ionization states of hafnium. Keywords:
X-ray spectra; Band structure; Quasi-relativistic
The X-ray spectrum ments
is of great
of highly
interest
ionized
in plasma
heavy
diagnostic
configuration; Interaction theory
elestud-
ies in inertial confinement fusion experiments and Xray laser studies [ 1,2]. Recently, many X-ray spectra of heavy elements have been identified as belonging to the isoelectronic sequence of NiI and neighbouring ionization states [ 3-101. Investigations for highly ionized hafnium atoms have been carried out for 3d4p transitions in the 7.0-8.0 A range [ 3,9], for 3d-4f transitions in the 6.1-6.6 A range [ 7,9] and for 3d-Sf transitions in the 4.6-5.0 8, range [ lo]. In the present Letter, we report an extended analysis of X-ray band spectra of highly ionized hafnium atoms from laser produced plasmas in the 4.1-4.5 A range. The experiments were performed at the Xing-Guang laser facility at the Institute of Nuclear Physics and Chemistry of the Chinese Academic of Engineering Physics (CAEP) . The beam of the frequency-doubled 0.53 pm Nd-glass laser was focused onto a solid planar target. The pulse length was 800 ps and the aver-
037%9601/96/$12.00
@
SSD/O375-9601(95)00901-9
age laser flux was lOI W/cm2. The emission spectra in the 4.1-4.5 8, range were observed by a PET ( 2d = 8.742 A) flat crystal spectrometer and recorded on Kodak AA5 film. The experimental spectra are shown in Fig. 1, the measured mean wavelengths and their full widths at half maxium (FWHM) of all peaks are given in Table 1. The uncertainties of the measured wavelengths are within f0.003 A in the experiments. More details are given in Ref. [ 91. In the present Letter, calculations of wavelengths and transition probabilities are made out using Cowan’s code [ 111 including configuration interaction and relativistic corrections. Our calculations show that the observed spectra are due to 3d-6f transitions of NiI and low ionized states CuI-GeI of the hafnium atom. As the differences between the binding energies of the 4s, 4p, 4d etc. electrons are small compared to the plasma temperature, many possible transition arrays have been considered in the calculations. It is found that the transition lines belonging to
I996 Elsevier Science B.V. All rights reserved
C. Dong et al./ Physics Letters A 210 (19%) 195-197
196
Ij(A)
=C1c(l\i)exp(-41n{2[(A-Ai)/S]2}) i
X
exp(
-fiE;/KT,),
(1)
where 10( Ai) is the theoretical transition probability at wavelength Ai, K is the Boltzmann constant, AE; is the energy spread of the upper configuration, and T, is the temperature of the electrons of the plasma. The summation is performed only for overlapping lines having large transition probabilities. Under the high temperature condition, AEi < KT,, the Boltzmann factor exp( -A,!$/KT,) tends to unity. Considering the overlapping of the different ionization state spectra, the intensity of the theoretical spectrum is calculated as I(A)
I
4.1
I
I
4.2
4.3
Wavelength Fig.
1.Experimental
4.4
4.5
( W)
spectrum (solid line) and theoretical spectrum
(dashed line) of highly ionized hafnium atoms in the 4.1-4.5
%,
wavelength range. The numbers correspond to the labels in Table
the different ionization states are separated, but those of the same ionization state are nearly superimposed and not distinguishable from one another according to directly calculated data for individual lines, except for two strong lines of the 3d”-3d96f transition of the Ni-like ionization state which involved only one single 3d inner-shell electron excitation. In order to interpret the band structure features of the observed spectra, we consider the broadening of the individual lines and overlapping of a large number of transition lines in the ionization states. We assumed for each broadened line a Gaussian shape and a FWHM of S, in the local thermodynamic equilibrium approximation. The intensity of the overlapping spectra from a single ionization state j is given by
= C j
wjlj(A),
(2)
where the summation over j includes the possible ionization states in the plasma, wj is the weight factor of ionization state j, which can be estimated simply by comparing the intensity ratio of the theoretical peak with the experimental one. In the detailed calculations, the experimental widths (0.008 A) of the isolated 3ds/*-6fs,2 and 3d5/2-6f7,2 transitions of the Ni-like ion were used as S in Eqs. ( 1) and (2). In the case of the Cu-like ion, we calculate the 3d-6f transitions in the presence of a single 41 “spectator” electron (1 = s, p and d). For the Zn-like ion, we consider the spectator electron configurations 4s4p, 4s4d and 4p2. The 4s24p, 4s4p2 and 4p” spectators are included for the Ga-like calculation. The 4s24p2 spectator is considered in the calculation of the Ge-like spectrum. The comparison of our calculation results with experimental spectra is given in Fig. 1, where the weight factors Wj for the NiI-GeI ionization states are 1.0, 0.25,O. 10,0.07 and 0.04, respectively. The calculated mean wavelengths and the FWHMs of the band peaks are given in Table 1. It can be seen from Fig. 1 that the structure features of the observed spectra are in good agreement with the ab initio calculations. The differences between the computed mean wavelengths and observed ones, about 0.007 A, may be mainly due to some weak configuration interactions and residual relativistic effects which have not been included in the present calculations. In addition, the contributions of a large number of weak
C. Dong et al./Physics Table I The mean wavelengths Label
2 3 4 5 6 7 8 9 IO
Ion
Letters A 210 (1996) 195-197
and full width at half maxium of the peaks produced
197
by highly ionized hafnium
atoms in the 4.1-4.5
8, range
Transition
NiI Cul Nil ZnI
4.1 16 4.177 4.197 4.238
Cul Gal
4.257 4.295
Znl Gel Gal Gel
4.317 4.358 4.380 4.441
lines (their weight transition probabilities being less than 1 .O x 1014 SK’ ) have been neglected in the present synthetic spectrum. In conclusion, the X-ray spectra from a laser produced highly ionized hafnium plasma in the 4.1-4.5 A range have been obtained and identified as 3d-6f transitions from Ni-like to Ge-like ionization states. It is found that the traditional theoretical method used in the present analysis is still valid to interpret these complex spectra. In order to illustrate the validity, we have also carried out a similar calculation for highly ionized gold atoms. Our new results are in good agreement with the previous theoretical ones [5] of the spin-orbit splitting array (SOSA) model [ 121. An isoelectronic comparison shows that the structure features of the 3d-6f spectra of highly ionized hafnium atoms are similar to those of other high-Z elements reported in Refs. [ 5,681. Peaks corresponding to different ionization states are found to be well separated. They can therefore serve as an excellent means for the determination of ionization states of highly ionized heavy atoms. This work was supported by the Foundation of the Chinese Academy of Engineering Physics and the Natural Science Foundation of Gansu Province.
4.1 I1 4.169 4.190 4.228 4.25 I 4.294 4.3 I I 4.352 4.380 4.440
0.008 0.01 I 0.008 0.014 0.012 0.010 0.010 0.012 0.01 I 0.014
0.008 0.010 0.008 0.010 0.010 0.01 I
0.010 0.010 0.012 0.012
References [ 1] D. Mathews, in: Proc. 8th Int. Coil. on Ultraviolet and Xray spectroscopy of astrophysical and laboratory plasmas (Washington, DC, 1984). [2] S. Maxon, P Hagelstein, K. Read and J. Scofield, J. AppI. Phys. 57 (1985) 1706. [3] P. Mandelbaum and M. Klapisch, A. Bar-Shalom and J.-L. Schwab, Phys. Ser. 27 (1983) 39. [4] P. Audebert, J.-C. Gauthier, J.-I? Geindre, C. ChenaisPopovics, C. Bauche-Amoult, J.C. Bauche and M. Klapisch, Phys. Rev. A 32 (1985) 409. [5] A. Zigler, M. Klapisch and I? Mandelbaum, Phys. L&t. A I I7 (1986) 31. [6] C. Bauche-Amoult, E. Luc-Koenig, J.-F. Wyart, J.-P. Geindre, P, Audebcrt, I? Monier, J.-C. Gauthier and C. ChenaisPopovics, Phys. Rev. A 33 ( 1986) 791. [7] M. Klapisch, I? Mandelbaum, A. Zigler, C. Bauche-Amoult and J. Bauche, Phys. Ser. 34 ( 1986) 5 I. [S] N. Tragin, J.-P. Geindre, P Monier, J.-C. Gauthier, C. Chenais-Popovics, J.-F. Wyart and C. Bauche-Amoult, Phys. Ser. 37 ( 1988) 72. [9] Y.-Q. Zhou, B.-H. Zhang, G.-H. Yang, A.-L. Lci and C.-Z. Dong, Acta Phys. Sin. 43 ( 1994) 1624. [ IO] C.-Z. Dong, Y.-Q. Zhou and B.-H. Zhang, J. Phys. B ( 1995), to be published. [I I ] R.D. Cowan, The theory of atomic structure and spectra (University of California Press, Berkeley, I98 I ). [ 121 C. Bauche-Smoult, J. Bauche and M. Klapisch, Phys. Rev. A 31 (1985) 2248.