OBSERVATIONS OF THE EFFECT OF INCREASING CORE CHARGE ON RYDBERG SPECTRA IN THE Xe ISOELECTRONIC SEQUENCE

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OBSERVATIONS OF THE EFFECT OF INCREASING CORE CHARGE ON RYDBERG SPECTRA IN THE

Xe ISOELECTRONIC SEQUENCE

T. Mcilrath, T. Lucatorto

To cite this version:

T. Mcilrath, T. Lucatorto. OBSERVATIONS OF THE EFFECT OF INCREASING CORE CHARGE

ON RYDBERG SPECTRA IN THE Xe ISOELECTRONIC SEQUENCE. Journal de Physique Col-

loques, 1982, 43 (C2), pp.C2-255-C2-263. �10.1051/jphyscol:1982219�. �jpa-00221830�

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JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°ll, Tome 43, novembre 1982 page C2-255

OBSERVATIONS OF THE EFFECT OF INCREASING CORE CHARGE ON RYDBERG SPECTRA IN THE Xe ISOELECTRONIC SEQUENCE

T . J . Mcllrath and T.B. Lucatorto*

national Bureau of Standards and University of Maryland, College Park, MD 20742, U.S.A.

*National Bureau of Standards, Washington, D.C. 202S4, U.S.A.

Résumé. Le spectre de Rydberg et les états autoionisants peuvent exhiber de grandes variations au long d'une séquence isoélectronique. Ces variations manifestent l'effet de la structure du coeur sur les états de Rydberg. Nous avons obtenu le spectre de Ba en absorption et nous le comparons avec le spectre isoélectronique du Xénon. La très importante diminution de la largeur d'autoionisation avec l'aug- mentation de la charge du coeur est expliquée à l'aide d'une analyse basée sur la théorie MQDT. On montre que les largeurs d'autoionisation sont un test sensible de l'importance des corrélations et de la dépendance des termes le long d'une séquence isoéléctronique.

Abstract. The Rydberg spectra and autoionizing levels of atoms can show large variations along an isoelectronic sequence. These variations reflect the effect of core structure on high lying levels. We have obtained the spectrum of Ba+ + in absorption and compare it with the isoelectronic Xe spectrum. The dramatic decrease in autoionization width with increasing core charge is explained through an analysis based on MQDT. The autoionizing widths are shown to be an especially sensitive indicator of the importance of

correlations and term dependence along the isoelectronic sequence.

I. Introduction

In this paper we will be discussing the behavior of Rydberg states along an isoelectronic sequence. A Rydberg atom is an atom with an electron orbiting at a large radius so that the ionic core looks more and more like a point charge. -It is therefore striking that the study of Rydberg states, and more especially autoionizing states, can provide us with rich information concerning the ionic core. We can get an indication of this by looking at the Rydberg levels of the rare gas atoms. These atoms have an np° ^ S Q ground state and five Rydberg series going to the spin-orbit split np~> P3/2 an<i ^ 1 / 2 final states. The Rydberg series for Ne and Xe going to the second limit are shown in figure 1. Both spectra are unpublished results by K. Yoshino. Special attentionois drawn to the nd' series. In Ne the lines are instrumentally limited (=.006 A) almost from the beginning while in Xe the autoionizing widths are a significant fraction of the level spacing as far as the series is traced. This difference comes from the structure of the core. The structure of the core manifests itself in the quantum defects of the bound states and in the autoionization widths of the states above the first series limit.1 In fact, the quantum defects and the autoionization widths are closely related, as is made clear by a Multichannel Quantum Defect Theory (MQDT)2 analysis. In this paper we will illustrate the effect of the core structure more clearly by comparing the isoelectronic spectra, more specifically the spectra of Ba+ + and Xe, and by analyzing them using MQDT.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982219

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JOURNAL DE PHYSIQUE

Figure 1. Upper spectrum Ne Rydberg series going to zp5 'plI2 limit.

Lower spectrum Xe Rydberg series going to 5p5 2~1/2 limit.

1 1 .

Experiment

High lying Rydberg states, and more especially autoionizing states, are most easily studied in absorption. This has limited earlier Rydberg studies to neutral metals and the rare gas atoms. Recently a technique3 has been developed for produc- ing relatively dense, well characterized, columns of ionic species which allows absorption studies of Rydberg series and photoionization continua. In these experiments a well-defined column of metal vapor is produced in a heat-pipe oven.

The vapor is then irradiated with a laser, tuned to the resonance line of the atoms, which saturates the transition and equalizes the population in the ground and first excited states. At the same time various processes produce a greater or smaller number of free electrons. The bound electrons are held at a high efgective temperature by the incident radiation, and collisions of the free electrons'with the neutral atoms transfers this excitation to the free electrons through superelastic collisions. The free electrons heat and subsequently multiply by collisional ionization, finally resulting in almost complete ionization (9525%) of the metal vapor. The entire process occurs in a fraction of a microsecond, during which time the heavy ions are effectively stationary. The result is an ion column of known density with a low excitation and Doppler temperature. This technique has now been studied by several experimenters using most of the alkali and alkaline earth elements.4 If the ion has an accessible resonance line, then it can subsequently be excited and driven to the next stage of ionization.

.Figure

2

shows the energy levels of Ba and ~ a + with their resonance lines at

5537A and

4935A.

The structure of of Ba

is

that of a Xe core with two valence elec-

trons in the 6s shell so that Ba++, produced by exciting first Ba and then ~ a + , is

isoelectronic to Xe.

A

schematic of the apparatus for the study of Ba ions is shown

in figure

3.

The two flashlamp pumped dye lasers are sequentially pumped to produce

Ba++ in ~ 1 0 - 6 sec and a photographic spectrum is subsequently recorded with a BRV

background spark

("70

ns d~ration)~ and a 3m grazing incidence spectrograph. The

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Figure 2. Partial level diagram of Ba and ~.'a

TOROIDAL MIRROR CAPILLARY

PULSE.FORMlNG

5537A LASER DICHROIC MiRROR

GENERATOR

Figure 3. Experimental schematic of Laser driven ionization with sequential pumping of Ba and Ba+ to produce Ba++ with subsequent recording of far

W

absorption spectrum.

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9 10 I I 12 13 14 16

I I I I I

1 1 L I 1

370 360 350 340 330

WAVELENGTH ( 8 )

5 1 5 1

Figure 4. Absorption s p e c t r a from

sp6 'so

t o Sp n s P1 and 5p nd Pl going t o t h e 2~~~~ and 2 ~ 1 / 2 l i m i t s .

f i n a l sample c o n s i s t s o f a 12 c m column o f 22.5x 10'' d e n s i t y o f ~ a + + w i t h a l l t h e p o p u l a t i o n i n t h ground s t a t e . A microdensitometer t r a c i n g o f t h e a b s o r p t i o n spectrun from t h e 5p

8

s h e l l i s shown i n f i g u r e 4 .

111. MQDT Analysis o f ~ a + + and Xe S p e c t r a

The Rydberg s e r i e s from t h e

sp6 'so

ground s t a t e o f Xe-like atoms and, i o n s involve f i v e i n t e r a c t i n g channels:

sp6+

5pS [ 2 ~ 3 / 1 ~ n s ~ , ~ , ndSl1, ndSL2 and Sp6+ Sps [2~1/2] ns71/2. n d t 3 i 2 . Terms belonging t o t h e first t r e e c a n n e l s d e s c r i b e Rydberg s e r i e s converging t o $e 2 ~ 3 / 2 l i m i t I while t h e l a s t two channels d e s c r i b e two s e r i e s converging t o t h e l i m i t 12. Above t h e I~ l i m i t t h e n s * and ndl s e r i e s a r e embedded i n t h e conti%& o f t h e f i r s t t h r e e channels and $ r e t h e r e f o r e s u b j e c t t o a u t o i o n i z a t i o n .

In o r d e r t o p u t t h e s p e c t r a on t h e same energy s c a l e and t o remove t h e e f f e c t o f d i f f e r i n g n u c l e a r charge they can be p l o t t e d a g a i n s t e f f e c t i v e quantum number.

The e f f e c t i v e quantum numbers vl and _-

v2

_-a r e defined by t h e r e l a t i o n s h i p

2 2 2

5 w f I 1

-

RJvl and *to= I2

-

5 IWv; with -hw being t h e i n c i d e n t photon energy,

5

t h e charge s t a t e i n t h e c o r e and %, t h e Rydberg c o n s t a n t . Figure 5 shows t h e a u t o i o n i z i n g resonances i n a segment o f t h e Xe and Ba++ photoabsorption s p e c t r a a s a f u n c t i o n o f t h e e f f e c t i v e quantum number ~ 2 .

The c o n t r a s t between t h e two s p e c t r a i s remarkable, e s p e c i a l l y c o n s i d e r i n g t h a t we a r e d e a l i n g with Rydberg l e v e l s a t t a c h e d t o c o r e s having t h e same c o n f i g u r a t i o n . I n p a r t i c u l a r , two f e a t u r e s a r e t o be ~ o t e d : The dramatic d e c r e a s e i n t h e a u t o - i o n i z i n g widths o f t h e n d ' s e r i e s w i t h i n c r e a s i n g charge s t a t e 5 o f t h e c o r e , and t h e s u b s t a n t i a l s h i f t i n t h e p o s i t i o n s of t h e n s * resonances. These f e a t u r e s a r e r e l a t e d t o changes i n c o r r e l a t i o n and term-dependence along t h e i s o e l e c t r o n i c sequence and can b e s t be understood w i t h i n t h e framework of MQDT.

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Figure 5. Photoabsorption s p e c t r a o f Xe and ~ a * + , above t h e first i o n i z a t i o n l i m i t , p l o t t e d versus e f f e c t i v e quantum number v

2

-

MQDT u t i l i z e s t h e p r o p e r t i e s of t h e s c a t t e r i n g e i g e n f u n c t i o n s o f t h e system of

COE p l u s e l e c t r o n and o f t h e Coulomb wave f u n c t i o n s i n o r d e r t o c h a r a c t e r i z e t h e e n t i r e spectrum by a few dynamical parameters. These parameters a r e t h e phase s h i f t s o f t h e s c a t t e r i n g e i g e n f u n c t i o n s (designated a s

w a

where

vcL

a r e t h e eigenquantum d e f e c t s ) , t h e u n i t a r y t r a n s f o r m a t i o n matrix Ui, which connects t h e

d i s s o c i a t i o n channel eigenfunctions w i t h t h e s c a t t e r i n g e i g e n f u n c t i o n s and t h e eigenamplitudes ,D which a r e t h e d i p o l e moments between t h e ground s t a t e and t h e s c a t t e r i n g e i g e n f u n c t i o n s . These parameters, pa, Ui, and D,, which a r e slowly varying f u n c t i o n s of energy, t o g e t h e r with t h e p o s i t i o n o f t h e s e r i e s l i m i t s , f o r m t h e b a s i s f o r a complete d e s c r i p t i o n o f t h e d i s c r e t e and continuous components of t h e Rydberg spectrum. I t should be noted t h a t t h e p a r e phase s h i f t s f o r p h y s i c a l l y r e a l c o l l i s i o n s t a t e s o n l y above t h e second P i m i t .

The bound s t a t e wave f u n c t i o n s o u t s i d e t h e c o r e a r e determined by t h e boundary c o n d i t i o n s t h a t t h e wave f u n c t i o n s vanish a t l a r g e r and t h a t t h e y have a phase s h i f t Irp r e l a t i v e t o hydrogenic f u n c t i o n s . T h i s phase s h i f t , o r quantum d e f e c t p, r e f l e c t s t h e e f f e c t o f t h e complex i o n i c c o r e and r e p l a c e s t h e hydrogenic requirement t h a t

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C2-260 JOURNAL DE PHYSIQUE

t h e Coulomb f u n c t i o n be r e g u l a r a t r = ^0. Thus t h e e n t i r e e f f e c t o f t h e c o r e on t h e Rydberg energy l e v e l s i s included i n t h e quantum d e f e c t .

In o r d e r t o pursue t h e s e i d e a s more q u a n t i t a t i v e l y we c o n s i d e r t h e Lu-Fano p l o t s f o r t h e Rydberg l e v e l s . A p l o t o f t h e r e l a t i o n s h i p between t h e e f f e c t i v e quantum numbers f o r t h e d i s c r e t e l e v e l s , v l and V i , with V 1 (mod 1 ) a s t h e o r d i n a t e and v2 (mod 1 ) a s t h e a b s c i s s a i s a Lu-Fano p l o t . The quantum d e f e c t vl is o n l y d e f i n e d f o r t h e d i s c r e t e s t a t e s up t o t h e f i r s t l i m i t 11, b u t a fundamental r e l a t i o n - s h i p of MQDT s t a t e s t h a t v1 below I1 i s e q u i v a l e n t t o t h e phase s h i f t ^Tof t h e continuum s c a t t e r i n g e i g e n s t a t e s above I1 up t o a f a c t o r n. Thus ~ / n (mod 1) p l o t t e d v e r s u s v2 w i l l f a l l on t h e same Lu-Fano p l o t a s defined by t h e bound s t a t e s and t h e p l o t g i v e s phase s h i f t s v e r s u s energy f o r t h e s c a t t e r i n g s t a t e s . The s c a t t e r i n g eigen- s t a t e s between t h e limits a r e composed p r i m a r i l y o f t h e t h r e e continuum channels azd t h e phases of t h e s c a t t e r i n g s t a t e s go through r a p i d changes by a i n passing through resonances w i t h t h e bound channels. The phase s h i f t curves do n o t c r o s s and t h e p o s i t i o n o f t h e resonances a r e e a s i l y seen on t h e Lu-Fano p l o t s . The degree o f avoided c r o s s i n g o f t h e phase s h i f t curves determines t h e r a t e of change o f t h e phase s h i f t s i n going through t h e s t e p changes of a and is a measure of t h e a u t o i o n i z a t i o n

width^.^

I n t h i s way t h e Lu-Fano p l o t , o b t a i n e d from bound s t a t e quantum d e f e c t s , i s used t o g e t t h e p o s i t i o n and widths o f t h e a u t o i o n i z i n g resonances above t h e f i r s t l i m i t .

I n F i g u r e 6 we show t h e Lu-Fano p l o t s f o r Xe and ~ a + + a s obtained from bound s t a t e d a t a along with a segment of t h e a b s o r p t i o n spectrum p l o t t e d v e r s u s v2. The o r d i n a t e i s t h e quantum d e f e c t (mod 1) f o r t h e bound s t a t e s and t h e phase s h i f t (mod a ) f o r t h e continuum s t a t e s . A s one can s e e , t h e quantum d e f e c t curves indeed go through r a p i d changes near t h e n s f and ndt resonances. Also, t h e r e a r e l a r g e avoided c r o s s i n g s between t h e Sp5 nd channels i n Xe where t h e nd' resonances a r e broad and t h o s e avoided c r o s s i n g s a r e s u b s t a n t i a l l y reduced i n Ba++ where t h e n d f resonances a r e narrow. I n c o n t r a s t , t h e avoided c r o s s i n g s between t h e n s channels a r e small f o r both c a s e s . MQDT p r e d i c t s t h a t : i ) t h e v a l u e o f t h e eigenquantum d e f e c t s pa f o r t h e s c a t t e r i n g e i g e n s t a t e s (not t h e j j coupled s t a t e s ) l i e a t t h e i n t e r s e c t i o n s o f t h e quantum d e f e c t curves t / a w i t h t h e diagonal l i n e r / n + v 2 = 1, and i i ) t h e i n t e r a c t i o n between two jj-coupled channels a r e weak i f t h e corresponding avoided c r o s s i n g t a k e s p l a c e away from t h e d i a onal line.' s e e s t h a t t h e avoided c r o s s i n g s between t h e 5p n s and t h e sp5 nd channels a r e

!

From the Lu-Fano p l o t s one small and a r e always l o c a t e d away from t h e diagonal l i n e . On t h e o t h e r hand, t h e diagonal l i n e i n t e r s e c t s t h e quantum d e f e c t curves o f t h e 5p5 nd channels a s well a s

t h o s e of t h e 5p n s channels a t t h e i r r e s p e c t i v e avoided c r o s s i n g s . As a re:ult, -3

t h e d i f f e r e n c e s between t h e eigenquantum d e f e c t s o f t h e s e i n t e r a c t i n g channels which determines t h e avoided c r o s s i n g a l s o determines t h e a u t o i o n i z i n g widths o f t h e n d t and n s f resonances. The decrease i n t h e widths o f t h e n d f l e v e l s i n going from Xe t o ~ a + + t h u s r e f l e c t s t h e l a r g e d e c r e a s e i n t h e s t r e n t h o f t h e avoid c r o s s i n g s o f

E

t h e

sp5

nd channels. The avoided c r o s s i n g o f t h e 5p n s channels is small i n both Xe and Ba++ s o t h a t even though t h e r e i s a s t r o n g channel i n t e r a c t i o n t h e auto- i o n i z a t i o n widths a r e small.

IV. C o r r e l a t i o n s , Term Dependence and E f f e c t i v e P o t e n t i a l s

The MQDT a n a l y s i s i s u s e f u l t o show t h e connections between a u t o i o n i z i n g widths and t h e quantum d e f e c t d i f f e r e n c e s between i n t e r a c t i n g channels. I t now remains f o r u s t o d e s c r i b e how t h e quantum d e f e c t s a r e a f f e c t e d by changing c o r r e l a t i o n e f f e c t s along t h e i s o e l e c t r o n i c sequence.

I n t h e lowest o r d e r c a l c u l a t i o n e l e c t r o n s move i n an e f f e c t i v e p o t e n t i a l Veff a r i s i n g from a c e n t r a l p o t e n t i a l V i and t h e c e n t r i f u g a l b a r r i e r ~ ( 1 1 + 1 ) 3 ~ / 2 m r ~ . ^A b e t t e r approximation i s t h e tern-dependent Hartree-Fock c a l c u l a t i o n where diagonal coupling terms a r e included t o account f o r exchange e f f e c t s and o f f diagonal terms a r e

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Figure 6. Lu-Fano p l o t obtained from bound s t a t e s compared w i t h a b s o r p t i o n c r o s s - s e c t i o n s v e r s u s v2 above t h e f i r s t i o n i z a t i o n l i m i t f o r Xe ( l e f t ) and Ba++ ( r i g h t ) .

included t o account f o r channel i n t e r a c t i o n s and c o r r e l a t i o n e f f e c t s . The

importance of t h e channel i n t e r a c t i o n s and t h e exchange e f f e c t s has t o be measured by a comparison o f t h e i r s t r e n g t h t o t h e s t r e n g t h o f t h e c e n t r a l p o t e n t i a l term.

In f i g u r e 7, t h e e f f e c t i v e p o t e n t i a l Veff f o r t h e

sp5

nd channels a r e shown f o r Xe, CS+ and ~a'". One s e e s t h a t t h e r e i s a v e r y shallow p l a t e a u i n t h e e f f e c t i v e p o t e n t i a l o f Xe and t h a t t h i s p l a t e a u - l i k e s t r u c t u r e g r a d u a l l y d i s a p p e a r s i n t h e e f f e c t i v e p o t e n t i a l s of csi and Ba++. The p l a t e a u i n t h e e f f e c t i v e p o t e n t i a l of Xe a r i s e s from a near c a n c e l l a t i o n between t h e c e n t r a l p o t e n t i a l and t h e c e n t r i f u g a l b a r r i e r i n t h e v a l e n c e region. The r e s u l t i s t h a t t h e Xe p o t e n t i a l i s very s e n s i t i v e

t o otherwise small p e r t u r b a t i o n s such a s Hartree-Fock exchanges and e l e c t r o n

c o r r e l a t i o n s . I n terms of t h e s c a t t e r i n g p i c t u r e , low energy e l e c t r o n s spend a long time t r a v e r s i n g t h e p l a t e a u r e g i o n and small d i f f e r e n c e s i n t h e depth o f t h e p o t e n t i a l r e s u l t i n l a r g e phase s h i f t d i f f e r e n c e s . T h i s i s shown i n t h e f a c t t h a t c o r r e l a t i o n e f f e c t s r e s u l t i n l a r g e phase s h i f t d i f f e r e n c e s between t h e t h r e e e x c i t e d d - o r b l t a l s i n Xe and t h a t t h e s e d i f f e r e n c e s d e c r e a s e r a p i d l y with i n c r e a s i n g charge s t a t e a s t h e c e n t r a l p o t e n t i a l becomes more and more dominant. By c o n t r a s t , t h e r e i s no c e n t r i f u g a l b a r r i e r i n t h e

spS

n s channels and t h e phase s h i f t d i f f e r e n c e between t h e e x c i t e d s - o r b i t a l s i s small and v a r i e s slowly along t h e i s o e l e c t r o n i c sequence.

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I t is t h e l a r g e d i f f e r e n c e i n phase s h i f t between t h e d-channels which m a n i f e s t s i t s e l f i n t h e l a r g e widths o f t h e a o t o i o n i z i n g s t a t e s i n Xe. The d e c r e a s i n g d i f f e r e n c e i n phase s h i f t w i t h i n c r e a s i n g charge s t a t e r e s u l t s i n t h e decreased d-channel widths f o r Ba++. I n each c a s e t h e a u t o i o n i z i n g widths r e f l e c t t h e importance of c o r r e l a t i o n s i n the s p e c i e s being considered.

4

-

Xe -

- -

- - _-

- -

-

L

V

3

*

-- -

( 1 1 ! ! I

I J f !

0 2 4 6 8

r ( B o h r r a d i u s )

5 p -+ d CHANNELS

Figure 7. E f f e c t i v e p o t e n t i a l curves establishec' by RRPA c a l c u l a t i o n s f o r Xe, CS+ and Ba++.

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V . Summary

In summary, we p r e s e n t h e r e t h e first experimental s t u d i e s o f a u t o i o n i z i n g s e r i e s along a n i s o e l e c t r o n i c sequence and t h e r e s u l t s o f a t h e o r e t i c a l a n a l y s i s which a c c u r a t e l y e x p l a i n s t h e o b s e r v a t i o n s . The t h e o r e t i c a l a n a l y s i s is based on a n MQDT approach and shows t h a t t h e dramatic d e c r e a s e i n t h e width o f t h e d-channel a u t o i o n i z i n g resonances i s t h e result of a d e c r e a s e i n s e n s i t i v i t y t o e l e c t r o n - e l e c t r o n c o r r e l a t i o n s w i t h i n c r e a s i n g charge s t a t e . We s e e t h a t s t u d i e s o f

a u t o i o n i z i n g t r a n s i t i o n s i n i s o e l e c t r o n i c sequences provides a n e s p e c i a l l y s e n s i t i v e measure of t h e s e changes i n c o r r e l a t i o n and term dependence a s a f u n c t i o n o f c o r e charge s t a t e .

The a u t h o r s would l i k e t o acknowledge W. H i l l , J. Sugar, K. T. Cheng, and W. R. Johnson f o r long d i s c u s s i o n s d u r i n g t h e development of t h e s e i d e a s and Dr. K. Yoshino f o r providing h i s Ne and Xe s p e c t r a .

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