- Email: [email protected]
Photodetachment of the H- ion
Volume 150, number 1
PHYSICS LETTERS A
Photodetachment
22 October 1990
of the H- ion
S.M. Burkov a,b, N.A. Letyaev a and S.I. Strakhova a a Institute ofNuclear Physics, Moscow State University, Moscow 119899, USSR b Khabarovsk Polytechnical Institute, Khabarovsk 680035, USSR Received 23 July 1990; accepted for publication 27 August 1990 Communicated by B. Fricke
The photodetachment cross section of H-, the characteristics of autodetaching resonances below the n= 3 threshold, the anisotropy parameters in the angular distribution of photoelectrons and secondary photons, and the 2p/2s branching ratio are calculated in the six-state R-matrix approach. Comparison is made with experimental results.
The continuum of the H- ion has a qualitative distinction as compared with other helium-like systems: the finite number of resonances in series [ 11, the shape resonance just above the second threshold [ 2,3], etc. We present the results of our calculation of the H- photodetachment in the region of autodetaching resonances (ADR) below the n = 3 threshold, made in the R-matrix approach [ 41. We used the close-coupling approach of six ( 1s-~s-~P-~s-~P3d) states, retained twenty-five continuum orbitals in each channel, set the R-matrix radius equal to 38 a.u. and used the exact wave function for the residual H atom. All our results are given with respect to the conventional binding energy of the H- ground state - 0.52775 1 a.u. [ 5 1. The ADR parameters were obtained from the least squares fit of the calculated cross sections, using the modified Fano expression 1671: a(E) = (S, +S,e+S2E2)
(
1 -p2+p
2
>
where
E=2E-Er
.
The’angular distribution of photoelectrons for linearly polarized exciting radiation is determined by the expression Elsevier Science Publishers B.V. (North-Holland)
-&[ 1 +/P,(cost?)]
(2)
.
We calculated the anisotropy parameters /? by the well-known expression (see, for example, ref. [ 8 ] ). The angular distribution of secondary photons d WY/ dQ is proportional to 1 -(Y cos 213,where the anisotropy parameter cy was calculated by the following expression:
(3) which is analogous to that given in ref. [ 91. Here PL is the degree of linear polarisation of the exciting radiation (in the present calculation it was equal to unity), Azo is the alignment of the residual H atoms in the 2p state, which is A,,=$
(la)
r
=
0.502pm
(q+&12 )
Ez+1
g
+0.0502,
~2pes + 022ped
’
(4)
where c,,~,~ is the partial photodetachment cross section leaving the residual H atoms in the individual n/-state and a photon with angular momentum I’. Fig. 1 shows the total H- photodetachment cross sections. A slight difference in the cross sections calculated with length (L) and velocity (V) forms of the dipole transition operator may be induced by the completeness of the basis used. On this account, perhaps, we obtained somewhat higher, as compared 31
Volume 150, number 1
22 October 1990
PHYSICS LETTERS A
Mb
0.
12.6
12.8
12.7
fLV
b Fig. 1. Total H- photodetachment cross sections: (e) ref. [ 111; ( x ) ref. [ lo], the normalization to our V cross section at E= 12.53 our calculation, L-variant; (---) our calculations, V-variant. eV; (-)
Table 1 ADR parameters in the total H- photodetachment (-0.527751
a.u.).
1 Ry = 13.6058435
cross sections. The ADR positions are given with respect to the HeV. The errors of measurements are given in brackets.
ground
state
N
Ref.
&(eV)
r (eV)
4
P2
so (Mb)
1
[II [lOI 1111
12.654 12.650( 1) 12.646(4)
0.0342 0.039(2) 0.0275(g)
-0.716(370) -0.81(8)
0.479(98) 0.440(18)
-
this paper: Lvar. V-var.
12.667 12.667
0.0379 0.0370
- 1.040 - 0.824
0.466 0.684
6.419 7.219
0.146 0.167
0.059 0.059
[II 1111
12.767 12.78
0.000245
this paper: Lvar. V-var.
12.772 12.772
0.00026 0.00025
- 3.469 -0.898
0.128 0.137
6.209 6.887
0.002 0.002
0.0 0.0
[II [III
12.840 12.834(4)
0.0019 0.0016(3)
-0.67(
0.424(76)
-
12.841 12.841
0.00158 0.00173
-0.635 -0.524
0.534 0.623
7.116 7.922
2
3
this paper: L-var.
V-var.
32
14)
& (Mb)
0.002 0.025
& (Mb)
-0.0005 0.0003
Volume 150, number 1
PHYSICS LETTERS A
22 October 1990
eV
12.8
12.6
Fig. 2.2p/2s branching ratio in the H- photodetachment, V-variant.
ergy E equal to 12.53 eV. Table 1 illustrates the ADR-parameters in the total photodetachment cross section. The profile in-
the results of other groups, values of the ADR positions. The data of ref. [ lo], obtained in relative units, are normalized to our V cross sections at en-
with
1.0 a
0.0
1
‘.x__
ZP / _--
” -I--_\ I/
---_-__A
I
I
1
12.6
12;7
12.8
ev
Fig. 3. Anisotropy parameter in the angular distribution of photoelectrons /3, V-variant.
33
22 October 1990
PHYSICS LETTERS A
Volume 150, number 1 0.5
0.0
I
’
I
. ,
, , ,
I
I
I
, .
12.60
,
, . , ,
12.70
,
.
, 12.80
ev
Ex Fig. 4. Anisotropy parameter in the angular distribution of secondary photons (Y.The same designation as in fig. 1.
dexes of all ADR are negative. Our results agree more ciosely, on the whole, with the data of ref. [ lo] for the lowest lying ADR, rather than with the data of ref. [ 111. The structures in the cross section with the decay width less than 10e4 eV are not discussed in the present paper. One can see from fig. 2 that the detachment of the double-excited H- ion leads mainly to the population of the 2p-state of the residual H atom. The anisotropy parameter in the angular distribution of photoelectrons /3, shown in fig. 3, is obviously of a resonance character. The angular distribution anisotropy increases sharply at the ADR locations, just as is the case in the He and Li+ photoionisation [ 12 1. The anisotropy of the angular distribution of secondary photons cr, plotted in fig. 4, is rather high everywhere, except for the windows of the resonances. The symmetry of the second ADR (the numbering from table 1) in the 2p/2s branching ratio and in the anisotropy parameters (Yand /3 differs from those of the first and third ADR. This indicates, in combination with its small width r, that the second ADR probably belongs to the negative series (see also the analysis made in ref. [ 111). The authors wish to express their gratitute to Pro34
fessor V.V. Balashov and to Drs. Yu.F. Smirnov, L.Ya Stotland and Yu.M. Shirokov for fruitful discussions. The calculations were made at the computer center of the Institute of Nuclear Physics of the Moscow State University.
References
[ 1 ] A. Pathak, A.E. Kingston and K.A. Benington, J. Phys. B 21 (1988) 2939. [2] J.T. Broad and W.P. Reinhardt, Phys. Rev. A 14 (1976) 2159. [ 3 ] D.W. MacArthur, K.B. Butterfield, D.A. Clark, J.B. Donahue, P.A.M. Gram, H.C. Bryant, C.J. Harvey, W.W. Smith and G. Comtet, Phys. Rev. A 32 ( 1985 ) 192 1. [ 41 K.A. Benington, PG. Burke, M. Le Doumeuf, W.D. Robb, K.T. Taylor and V.K. Lan, Comput. Phys. Commun. 14 ( 1978) 367. [ 51CL. Pekeris, Phys. Rev. 126 (1962) 1470. [6] H. Kossmann, B. KrSssig and V. Schmidt, J. Phys. B 21 (1988) 1489. [ 71 M. Zubek, G.C. King, P.M. Rutter and F.H. Read, J. Phys. B 22 (1989) 3397. [8]V.L. Jac0bsandP.G. Burke, J. Phys.B 5 (1972) L67.
Volume 150, number I
PHYSICS LETTERS A
[ 91 J. Jimenez-Mier, CD. Caldwell and D.L. Ederer, Phys. Rev. Lett. 57 (1986) 2260. [ 101s. Cohen, H.C. Bryant, C.J. Harvey, J.E. Stewart, K.B. Butterfield, D.A. Clark, J.B. Donahue, D.W. MacArthur, G. Comtet and W.W. Smith, Phys. Rev. A 36 ( 1987) 4728.
22 October 1990
[ 1 l] M.E. Hamm, R.W. Hamm, J. Donahue, P.A.M. Gram, J.C. Pratt, M.A. Yates, R.D. Bolton, D.A. Clark, H.C. Bryant, C.A. Frost and W.W. Smith, Phys. Rev. Lett. 43 ( 1979) 1715. [ 121 N.A. Letyaevand S.I. Strakhova, Phys. Lett. A 126 (1987) 8.
35
PHYSICS LETTERS A
Photodetachment
22 October 1990
of the H- ion
S.M. Burkov a,b, N.A. Letyaev a and S.I. Strakhova a a Institute ofNuclear Physics, Moscow State University, Moscow 119899, USSR b Khabarovsk Polytechnical Institute, Khabarovsk 680035, USSR Received 23 July 1990; accepted for publication 27 August 1990 Communicated by B. Fricke
The photodetachment cross section of H-, the characteristics of autodetaching resonances below the n= 3 threshold, the anisotropy parameters in the angular distribution of photoelectrons and secondary photons, and the 2p/2s branching ratio are calculated in the six-state R-matrix approach. Comparison is made with experimental results.
The continuum of the H- ion has a qualitative distinction as compared with other helium-like systems: the finite number of resonances in series [ 11, the shape resonance just above the second threshold [ 2,3], etc. We present the results of our calculation of the H- photodetachment in the region of autodetaching resonances (ADR) below the n = 3 threshold, made in the R-matrix approach [ 41. We used the close-coupling approach of six ( 1s-~s-~P-~s-~P3d) states, retained twenty-five continuum orbitals in each channel, set the R-matrix radius equal to 38 a.u. and used the exact wave function for the residual H atom. All our results are given with respect to the conventional binding energy of the H- ground state - 0.52775 1 a.u. [ 5 1. The ADR parameters were obtained from the least squares fit of the calculated cross sections, using the modified Fano expression 1671: a(E) = (S, +S,e+S2E2)
(
1 -p2+p
2
>
where
E=2E-Er
.
The’angular distribution of photoelectrons for linearly polarized exciting radiation is determined by the expression Elsevier Science Publishers B.V. (North-Holland)
-&[ 1 +/P,(cost?)]
(2)
.
We calculated the anisotropy parameters /? by the well-known expression (see, for example, ref. [ 8 ] ). The angular distribution of secondary photons d WY/ dQ is proportional to 1 -(Y cos 213,where the anisotropy parameter cy was calculated by the following expression:
(3) which is analogous to that given in ref. [ 91. Here PL is the degree of linear polarisation of the exciting radiation (in the present calculation it was equal to unity), Azo is the alignment of the residual H atoms in the 2p state, which is A,,=$
(la)
r
=
0.502pm
(q+&12 )
Ez+1
g
+0.0502,
~2pes + 022ped
’
(4)
where c,,~,~ is the partial photodetachment cross section leaving the residual H atoms in the individual n/-state and a photon with angular momentum I’. Fig. 1 shows the total H- photodetachment cross sections. A slight difference in the cross sections calculated with length (L) and velocity (V) forms of the dipole transition operator may be induced by the completeness of the basis used. On this account, perhaps, we obtained somewhat higher, as compared 31
Volume 150, number 1
22 October 1990
PHYSICS LETTERS A
Mb
0.
12.6
12.8
12.7
fLV
b Fig. 1. Total H- photodetachment cross sections: (e) ref. [ 111; ( x ) ref. [ lo], the normalization to our V cross section at E= 12.53 our calculation, L-variant; (---) our calculations, V-variant. eV; (-)
Table 1 ADR parameters in the total H- photodetachment (-0.527751
a.u.).
1 Ry = 13.6058435
cross sections. The ADR positions are given with respect to the HeV. The errors of measurements are given in brackets.
ground
state
N
Ref.
&(eV)
r (eV)
4
P2
so (Mb)
1
[II [lOI 1111
12.654 12.650( 1) 12.646(4)
0.0342 0.039(2) 0.0275(g)
-0.716(370) -0.81(8)
0.479(98) 0.440(18)
-
this paper: Lvar. V-var.
12.667 12.667
0.0379 0.0370
- 1.040 - 0.824
0.466 0.684
6.419 7.219
0.146 0.167
0.059 0.059
[II 1111
12.767 12.78
0.000245
this paper: Lvar. V-var.
12.772 12.772
0.00026 0.00025
- 3.469 -0.898
0.128 0.137
6.209 6.887
0.002 0.002
0.0 0.0
[II [III
12.840 12.834(4)
0.0019 0.0016(3)
-0.67(
0.424(76)
-
12.841 12.841
0.00158 0.00173
-0.635 -0.524
0.534 0.623
7.116 7.922
2
3
this paper: L-var.
V-var.
32
14)
& (Mb)
0.002 0.025
& (Mb)
-0.0005 0.0003
Volume 150, number 1
PHYSICS LETTERS A
22 October 1990
eV
12.8
12.6
Fig. 2.2p/2s branching ratio in the H- photodetachment, V-variant.
ergy E equal to 12.53 eV. Table 1 illustrates the ADR-parameters in the total photodetachment cross section. The profile in-
the results of other groups, values of the ADR positions. The data of ref. [ lo], obtained in relative units, are normalized to our V cross sections at en-
with
1.0 a
0.0
1
‘.x__
ZP / _--
” -I--_\ I/
---_-__A
I
I
1
12.6
12;7
12.8
ev
Fig. 3. Anisotropy parameter in the angular distribution of photoelectrons /3, V-variant.
33
22 October 1990
PHYSICS LETTERS A
Volume 150, number 1 0.5
0.0
I
’
I
. ,
, , ,
I
I
I
, .
12.60
,
, . , ,
12.70
,
.
, 12.80
ev
Ex Fig. 4. Anisotropy parameter in the angular distribution of secondary photons (Y.The same designation as in fig. 1.
dexes of all ADR are negative. Our results agree more ciosely, on the whole, with the data of ref. [ lo] for the lowest lying ADR, rather than with the data of ref. [ 111. The structures in the cross section with the decay width less than 10e4 eV are not discussed in the present paper. One can see from fig. 2 that the detachment of the double-excited H- ion leads mainly to the population of the 2p-state of the residual H atom. The anisotropy parameter in the angular distribution of photoelectrons /3, shown in fig. 3, is obviously of a resonance character. The angular distribution anisotropy increases sharply at the ADR locations, just as is the case in the He and Li+ photoionisation [ 12 1. The anisotropy of the angular distribution of secondary photons cr, plotted in fig. 4, is rather high everywhere, except for the windows of the resonances. The symmetry of the second ADR (the numbering from table 1) in the 2p/2s branching ratio and in the anisotropy parameters (Yand /3 differs from those of the first and third ADR. This indicates, in combination with its small width r, that the second ADR probably belongs to the negative series (see also the analysis made in ref. [ 111). The authors wish to express their gratitute to Pro34
fessor V.V. Balashov and to Drs. Yu.F. Smirnov, L.Ya Stotland and Yu.M. Shirokov for fruitful discussions. The calculations were made at the computer center of the Institute of Nuclear Physics of the Moscow State University.
References
[ 1 ] A. Pathak, A.E. Kingston and K.A. Benington, J. Phys. B 21 (1988) 2939. [2] J.T. Broad and W.P. Reinhardt, Phys. Rev. A 14 (1976) 2159. [ 3 ] D.W. MacArthur, K.B. Butterfield, D.A. Clark, J.B. Donahue, P.A.M. Gram, H.C. Bryant, C.J. Harvey, W.W. Smith and G. Comtet, Phys. Rev. A 32 ( 1985 ) 192 1. [ 41 K.A. Benington, PG. Burke, M. Le Doumeuf, W.D. Robb, K.T. Taylor and V.K. Lan, Comput. Phys. Commun. 14 ( 1978) 367. [ 51CL. Pekeris, Phys. Rev. 126 (1962) 1470. [6] H. Kossmann, B. KrSssig and V. Schmidt, J. Phys. B 21 (1988) 1489. [ 71 M. Zubek, G.C. King, P.M. Rutter and F.H. Read, J. Phys. B 22 (1989) 3397. [8]V.L. Jac0bsandP.G. Burke, J. Phys.B 5 (1972) L67.
Volume 150, number I
PHYSICS LETTERS A
[ 91 J. Jimenez-Mier, CD. Caldwell and D.L. Ederer, Phys. Rev. Lett. 57 (1986) 2260. [ 101s. Cohen, H.C. Bryant, C.J. Harvey, J.E. Stewart, K.B. Butterfield, D.A. Clark, J.B. Donahue, D.W. MacArthur, G. Comtet and W.W. Smith, Phys. Rev. A 36 ( 1987) 4728.
22 October 1990
[ 1 l] M.E. Hamm, R.W. Hamm, J. Donahue, P.A.M. Gram, J.C. Pratt, M.A. Yates, R.D. Bolton, D.A. Clark, H.C. Bryant, C.A. Frost and W.W. Smith, Phys. Rev. Lett. 43 ( 1979) 1715. [ 121 N.A. Letyaevand S.I. Strakhova, Phys. Lett. A 126 (1987) 8.
35