U P B an intemationui journal
Does hyperfine quenching affect significai|tly the level in He-like
•s
vanadium ? f
f
T N a n d t
Nuclear Science Center, Aruna Asaf Ali Marg, New Delhi-110 067, India E-mail : naiidi@nsc ernet in '
VhstrHCi ' Using a new method o f the beam-toil time-of-llight technique with a single, as well as a two-foil target, wc determined the lifciimc of the auto-ionizing \sls2p*P'^}/2 level in Li-like vanadium'a.<; 123 ± 10 ps. By accounting for the presence o f the unresolved Is2s2p*l*^iii satellite line in the M2 Is^ '5d - Is2/>'P” line, wc deduce a lifetime o f 314 ± 30 ps for the \s2p^P2 Hc-like vanadium level. This value is close to theoretical estimates without invoking hyperfine interactions into account rather than to the liypcrrmc quenched lifetime. It thus confirms that hyperfine quenching does not influence significantly the ls2p^P^ level lifetime in fle- hke vanadium. We have further developed an impirical formula to estimate the effective lifetime o f the ls2p '^Pf level if satellite is not
resolved in the experiment.
Keywords : Hyperfine quenching, lifetime, beam-foil time-of-flight technique, f v e s Nos. . 34.50.Fa. 32.30.Rj, 32.80.Ys
Inner shell v a c a n c ie s p r o d u c e d b y b e a m - f o il e x c ita tio n o f intermediate Z p r o j e c ti le s a r e e x p e c t e d to d e c a y w ith in o r very close to th e f o il, d u e t o t h e i r f a s t d e c a y v ia a u to ionization o r /a n d X - r a y e m is s io n . It is n o w w e ll e s ta b lis h e d , however, th a t m e ta s ta b le s t a te s w ith in n e r s h e ll v a c a n c ie s may be p r o d u c e d in a p p r e c i a b le n u m b e r s d u r i n g th e fo il excitation w i t h f a s t io n b e a m s . T h e b e s t u n d e r s t o o d metastable s ta te s b e lo n g to h y d r o g e n - a n d H e - lik c s y s te m s to their in a b ility t o d e c a y b y e le c tr ic d ip o l e e m is s io n , b e in g forced by s p in a n d p a r i ty s e le c tio n r u le s t o r a d ia te th r o u g h viewer, h ig h e r m u lti - p o l a r it ie s . In H e - lik e io n s h a v in g fin ite nuclear sp in a n d m a g n e t ic m o m e n t, th e h y p e r f in e in te r a c tio n induces a v e r y s m a ll m i x in g b e tw e e n \ s 2 p a n d \ s 2 p configurations t h a t r e d u c e s th e lif e tim e s o f th e \ s 2 p ^ P \ and \si2p le v e ls [1 ]. W e h a v e s h o w n th a t b le n d i n g d u e
•o the \s 2 s 2 p * P \ n - L i- lik e s a te llite lin e , i f n o t considered in t h e a n a ly s is o f th e d a ta , h a s a s i m i la r e f f e c t on the m e a s u r e d \ s 2 p ^ P \ lif e tim e . T h is in tu r n r e n d e r s problem atic a n y e x p e r i m e n t a l c tm f ir m a tio n o n th e e x te n t o f Ityperfine q u e n c h in g o n t h e I s ^ ® l®Yel lif e tim e s in H e -
lik e v a n a d iu m . W e u s e d th e b e a m - fo il tim e - o f - f lig h t te c h n iq u e w ith a s in g le - f o il [2 ], a s w e ll a s w ith a tw o - f o il ta r g e t [3 ] f o r th e firs t tim e to c ir c u m v e n t th e s a te llite b l e n d i n g in a n in n o v a tiv e w a y . A n a ly s is o f o u r d a ta d e m o n s tr a te d , f o r th e firs t tim e , th a t th e lo w life tim e , r e p o r te d in [2] f o r th e \ s 2 p ^ P \ le v e l in H e -lik e v a n a d iu m , a ris e s m a in ly fr o m u n a c c o u n te d b le n d in g d u e to th e \s 2 s 2 p *P%a ~ ^ S \a s a te llite lin e a n d is n o t d u e to h y p e r f in e q u e n c h in g . F u r th e r , o u r m e th o d p r o v id e s th e \ s 2 s 2 p *P%a l®Yel lif e tim e in L i- lik e v a n a d iu m b y d e te c tin g X - r a y s t h a t is p r o p o s e d a n d u ti li z e d f o r th e f ir s t tim e .
W e m a i n ly h a v e c o n f i r m e d th a t t h e li f e t im e o f th e l s 2 p ^P% s ta te is n o t a f f e c te d b y h y p e r f in e q u e n c h in g . T o r e a c h in to th e c o n c lu s io n w e h a v e m a d e u s e o f th e b e a m - fo il tim e - o f - f lig h t te c h n i q u e w ith s in g le - a s w e ll a s tw o - f o il ta r g e ts . N e ith e r th e b e a m - f o il ti m e - o f - f lig h t t e c h n i q u e w ith s in g le - f o il n o r th e b e a m - f o il ti m e - o f - f lig h t t e c h n i q u e w ith t w o - f o i l is n e w b u t u s i n g t h e t w o t e c h n i q u e s in o n e e x p e r i m e n t is e n ti r e l y n e w . I t is s o m e d iin g lik e th e in v e n to r y o f M u lti W ir e P r o p o r tio n a l C o u n te r (M W P C ) . S in g le w ir e
© 2002 lACS
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p r o p o r t i o n a l c o u n t e r w a s k n o w n b u t M W P C is j u s t c o m b i n a ti o n o f m a n y s in g le w ir e p ro p o r tio n a l c o u n te r s m a d e a r e v o l u ti o n in p h y s ic s . U s e o f b e a m - f o il ti m e - o f - f lig h t te c h n i q u e w ith s in g le - f o il a t tw o d if f e r e n t b e a m e n e r g ie s h a s in d ic a te d b le n d i n g o r c a s c a d e p r o b le m . T w o - f o il m e t h o d h a s p r o d u c e d a g r o w th s p e c tr u m w ith d is ta n c e . W e d o th in k th a t it is s e e n f o r t h e f irs t tim e . T h e a n a ly s e o f th e d a ta h a s b e e n d o n e in a n e w a n d n o v e l w a y . A s a r e s u lt w e s u c c e e d e d u n f o l d in g th e s a te llite b le n d in g p r o b le m th a t fo r c e d e a r lie r w o r k e r s [2] d r a w in g a h a r d c o n c lu s io n th a t h y p e r f m e fie ld q u e n c h e s th e \ s 2 p le v e l life tim e b y m o r e th a n 2 0 % . T h is r e s u lt w a s t h o u g h t a s h is to r ic a l a n d h a s b e e n p r o p a g a te d in m a n y te x t b o o k s a n d r e v e iw a r tic le s s u c h a s [ 4 - 1 1 ] ,
A r e c e n t w o r k [ 12] h a s c o n f ir m e d th a t th e lo w life tim e [2]
fo r th e \ s 2 p le v e l in v a n a d iu m w a s r e s u lte d d u e to th e e f f e c t o f s a te llite o f \s ^ 2 s ^ S \j2 - \ s 2 s 2 p V 5/2 b le n d e d w ith th e M 2 Is ^ *5o - \ s 2 p ^ P \ lin e . S a te llite lin e s o f th is ty p e w e r e r e s o lv e d in t h e X - r a y s p e c tr a o f A I [1 3 ] a n d N i [1 4 ], in w h ic h a D o p p le r tu n e d s p e c t r o m e te r a n d a h ig h r e s o lu tio n c r y s ta l s p e c t r o m e te r w a s u s e d , re s p e c tiv e ly . T h e H e - lik e M 2 lin e a n d its s a te llite d if f e r b y 4 3 e V (T a b le 1) in v a n a d iu m a n d a r o u n d th e s a m e in F e , N i, e tc a n d a re n o t r e s o lv e d b y s e m ic o n d u c t o r d e te c to r s . In th is c a s e , i f b le n d in g d u e to th e s a t e l l i t e l i n e is n o t t a k e n i n t o c o n s i d e r a t i o n in t h e m e a s u r e m e n ts , th e lif e tim e d e te r m in e d f r o m th e u n r e s o lv e d lin e m a y w e ll d e v ia te fro m th e tr u e v a lu e . W e h a v e d e v e lo p e d a n im p ir ic a l f o r m u la to s h o w h o w d o e s th is b le n d in g p ro b le m a f f e c t th e \ s 2 p ^ P \ le v e l lif e tim e in H e - lik e io n s.
Tabic I. Lifetimes for Hc-like and Li-like Nuclear spin 7/2, nuclear magnetic dipole moment - 5.15141 ^N.
Upper level
Line energy keV [18]
Beam energy (MeV)
Lifetime Expt. (ps) This work
Lifetime Theory
ps
X-ray Branching
ratio
\s2p^P% 5.1857 158 242 ± 5" 310 [17] 100%
322 ± 28* 242 [ l |
\s2s2p*P% n .5 1423 158 125 ± 1?< 155 [20] 37% [20]
159 [21] 34% [21]
157 [22]
ls2 p’ /*®2 5.1857 100 161 ± 5“ 310 [17] 100%
306 ± 32*' 242 [1]
ls2 s2 p * P % n 5.1423 100 121 ± 20" 155 [20] 37% [20]
ls2 p ^P% 314 ± 3Qf 310 [17] 100%
\s2s2p*P% 2 123 ± 19^ 15$ [20] 37% [20]
ls 2 p ^ P \ 5.1857 367 [2] 257 ± 5* 310 [17] 100%
ls2s2p*P%n 5.1423 367 [2] 173 ± 20* 155 [20] 37% [20]
‘Two-foil, data fitted with equation (1) (Decay fixed to 242 ps growing component was varied).
‘^Two-foil, data fitted with equation (1) (Decay fixed to I6i growing component was varied).
'Single foil, data fitted with two exponents {Xs2p^P\ was fixed 30^, ps and \sls2p^P%n was varied).
^Mcan o f the values obtained with the 158 MeV and 100 MeV beams
^Single foil data reported in [2], fitted with two exponents ‘ one for ihe M2, the other for the M l decay.
^Single foil data reported in [2], fitted with three exponents (lifetimes o f \s 2 p ^ P \ and ^25^51 fixed to 310 ps and 16.9 ns rcspcctiveh intensities fixed, and the \s2s2p^P%ri lifetime was varied)
T h e io n s u s e d in th e m e a s u r e m e n ts w e re obtained fr o m th e 16 M Y P c ile tr o n a c c e l e r a to r a t th e N u c le a r Science C e n tre , N e w D e lh i. A c o llim a te d , 3 m m - d ia m e te r , 158 MeV v a n a d iu m b e a m w a s e x c it e d b y p a s s a g e th r o u g h a 150 p g /c m ^ g o ld fo il. E m e r g in g X - r a y s w e r e p a s s e d th ro u g h a c o llim a tin g s y s te m c o n s i s ti n g o f th r e e s lits a s w ell as an X -ra y s h ie ld in g c u p a n d w e r e d e te c te d b y a low energv G e r m a n iu m d e te c to r ( r e s o lu tio n 1 5 0 e V a t 5 .9 k e V ) which w a s p la c e d a t r i g h t a n g le t o th e b e a m . T h e d im en sio n s 01 th e firs t slit (1 .6 m m x 8 m m ) w e re c h o s e n s o a s to en su n th a t o n ly th e X -ra y s fr o m fo il e x c ite d io n s r e a c h th e d e te cto r U n d e r th e s e e x p e r im e n ta l c o n d itio n s , g o ld X - r a y s w e r e m»i o b s e r v e d in th e s p e c tra . T h e m o v e m e n t o f th e foil wa^
c o n tr o lle d b y a p lu n g e r s y s te m , c o n s is tin g o f m ic ro steppci m o to rs . T ra v e rs a l o f th e p lu n g e r s y s te m w a s lim ited lo Ki m m . T h e b e a m w a s c o lle c te d in a n u n s u p p r e s s e d F aradas c u p b u ilt in to th e p lu n g e r . N o r m a liz a tio n o f th e in c id e n t ih \ w a s a c h ie v e d th r o u g h e la s tic s c a tte r in g o f th e b eam by a 1 2 0 p g /c m ^ g o ld fo il, 2 0 m m d o w n s tr e a m th e d e te c to r slit, re c o r d e d b y tv /o s ilic o n s u r f a c e b a r r ie r d e te c to r s th at were s y m m e tr ic a lly p la c e d a b o u t th e b e a m a x is . A sch em atic ol th e a p p a r a tu s is s h o w n in F ig u r e 1. P r o v is io n o f lo a d in g a tw o - f o il ta r g e t w a s k e p t in th e s e t u p , th u s m a k in g possible
^Single foil, data fitted with one exponent.
^Single foil, data fitted with two exponents (lifetime \s2p^P% o f was varied while that o f \s2s2p*P%f2 Fixed to 12^ ps).
I measurements o f
lifetimes
th a tare
a s sh o r t a sth a na
I picosecond
[3]. The experiment was repeated using a 100
: beam.
The s p e c t r u m , c a l i b r a t e d u s i n g a s t a n d a r d ^ ^ 'A m
radioactive
s o u rc e , e x h ib its tw o p r o m in e n t s p e c tra l lin e s, [.me identification w a s a c c o m p lish fe d [1 5 ] b y a s s o c ia tin g th e line at 5.17 k e V w ith th e tr a n s itio n '5 o - l s 2 p in H e - lil,e vanadium. T h e lin e a t 5.42 k e V ( F ig u r e 3, b e a m e n e rg y 158 MeV), w h ic h w a s n o t d is c e r n ib le a t 100 M e V , m a y tenutively b e a ttr ib u te d t o th e tr a n s itio n I s - 2s ^ S \a in H'like v a n a d iu m [ I S ] th a t p r o c e e d s v ia b o th M l a n d 2 E l modes,T he decay c u r v e s o f th e 5 .1 7 k e V lin e , a t b e a m e n e rg ie s of !0 0 M eV a n d 158 M e V , a re s h o w n in F ig u r e 3 f o r th e single foil e x p e rim e n t. T h e M 2 lin e d u e to th e Is^ -
\s lp ^ P \ tra n s itio n , th e M l lin e Is^ 'Sq - l s 2 s ^ S | a n d th e h y p e rfin e in d u c e d Is^ *5o - \s 2 p ^ P % d e c a y in H e - lik e vanadium a re n o t r e s o lv e d b y o u r d e te c to r. T h e life tim e o f I.s2.v \S'| [2] is la r g e a n d its e f f e c t o n th e d e c a y c u rv e d o e s not s h o w u p in th e lim ite d 10 m m tr a v e rs a l. T h e m e a n lifetim es f o r \ s 2 p ^P%, o b ta in e d b y f ittin g th e 5 .1 7 k e V d e c a y curves (F ig u re 3 ) w ith a s in g le e x p o n e n t, a re 2 4 2 ± 5 p s a n d 161 i 5 ps, re s p e c tiv e ly ( T a b le 1). W e a ls o fitte d th e 3 6 7 MeV data, r e p o r te d in [2 ] f o r th e 5 .1 7 k e V d e c a y , a n d obtained life tim e s o f 2 5 7 ± 5 p s fo r \ s 2 p ^ P \ a n d 1 6 .9 n s fo r I,v2s \
The v a ria tio n o f th e life tim e w ith th e b e a m e n e rg y is d u e 0 b le n d in g o r c a s c a d i n g e f f e c t s . H y p e r f i n e - i n d u c e d lorrections d o n o t d e p e n d o n th e p r o je c tile e n e r g y a n d th u s an n o t e x p la in th e o b s e r v e d v a r ia tio n . T o e x p lo r e th e c a u s e )f this v a r ia tio n , w e r e p e a t e d th e m e a s u r e m e n t o f th e s 2 p ^ p \ life tim e th r o u g h th e 5 .1 7 k e V d e c a y in H e -lik e
v a n a d iu m , th is tim e u s in g a tw o -f o il c a rb o n ta r g e t m e th o d [3 ]. In o u r e x p e rim e n t, th e m in im u m s e p a r a tio n b e tw e e n th e tw o s tre tc h e d fo ils w a s 115 p m . T h e firs t 3 5 p g /c m ^ c a rb o n fo il w a s m o v e d , w ith a p re c is io n o f 0 .5 m ic ro n s , w ith r e s p e c t to th e m u d i th in n e r (4 p g /c m ^ ) s e c o n d c a rb o n fo il. T y p ic a l s p e c tra a t ^ 8 M e V , o b ta in e d f o r d if fe re n t fo il s e p a r a tio n s , a re sh o w n | n F ig u r e 2 . A p e c u lia r fe a tu re o f th e s e s p e c tra is th e increi|B e in in te n s ity a t 5 .1 7 k e V w ith th e s e p a ra tio n
lOQOOi
Figrue 3. Single-foil experiment. Normalized count rate vs distance between the target foil and the detector for the 5.17 keV vanadium line. The zero corresponds to 5.6 mm in the 158 MeV experiment and to 2 mm in the 100 MeV experiment. The solid lines were obtained by fitting the data using a single exponent, the dashed lines using two exponents.
b e tw e e n th e tw o fo ils. A s a re s u lt, a g ro w in g fu n c tio n a p p e a rs c le a rly in th e c o rr e s p o n d in g d e c a y c u rv e a t 158 M e V a s sh o w n in F ig u r e 4 . H o w e v e r, th e d e c a y c u rv e a t 1 00 M e V is q u ite d iffe re n t. In th is c a s e w e o b s e r v e a n in itia l d e c re a s e in in te n s ity , fo llo w e d b y a s a tu r a tio n a s th e s e p a r a tio n
2. X-ray spectra with 158 MeV V beam obtained using a two- carbon target, for three different foil separations. The detector
^ kept at 5.6 mm from the second foil.
Figure 4. Two-foil experiment. Normalized count rate vs distance between the two foil for the 5.17 keV vanadium line. The detector was kept at a distance o f 5.6 mm from the second foil for the 158 MeV (upper curve) and at 4 mm for the 100 MeV (lower curve) experiments. The solid lines are the fits to the data.
410 T Nandi
in c r e a s e s . T h is c o n tr a s ts Oie p a tte rn o b s e r v e d a t 15 8 M e V ( F ig u r e 4 ) . B o th d e c a y c u r v e s h o w e v e r in d ic a te c le a r ly th e p r e s e n c e o f a g r o w in g fu n c tio n . In a n e a r lie r s tu d y [1 6 ], th e in f lu e n c e o f c a s c a d e e f f e c ts o n b e a m - f o il tim e - o f - f lig h t m e a s u r e m e n ts h a s b e e n e lim in a te d b y a p r o p e r c h o ic e o f th e b e a m e n e r g y . I n th e c u r r e n t s tu d y h o w e v e r, th e g ro w th in th e 5 .1 7 k e V d e c a y c u r v e ( F ig u r e 4 ) is n o t d u e to c a s c a d e e ff e c ts . W e a tt r i b u te th is g r o w th to b le n d in g a n d p r o c e e d to d is c u s s its o r ig in .
V a r io u s c h a r g e s ta te s a re p r o d u c e d w h e n a n io n b e a m p a s s e s t h r o u g h a fo il. F o r th e c a s e o f th e 1 5 8 M e V v a n a d iu m io n b e a m , H - to N - I ik e io n s a r e p r e s e n t o n e x it fr o m th e 3 5 p g /c m ^ c a r b o n f o il ( [ 1 9 ] ) , c o d e E T A C H A ) . P r o m in e n t f r a c tio n s a re H e -lik e ( 2 2 % ), L i-lik e (3 6 % ), a n d B e -lik e (2 6 % ).
T h e a u to i o n iz i n g s ta te s g e n e r a te d b y c o llis io n s w ith th e f ir s t c a r b o n fo il d e c a y to th e n e x t h ig h e r io n ic s ta te b e fo r e th e y r e a c h th e s e c o n d fo il. In p a r tic u la r , a u to io n iz in g s ta te s o f L i- lik e io n s p r o d u c e H e - lik e io n s in th e '5o le v e l.
T h e s e g r o u n d s t a te H e - lik e io n s a re e x c ite d to \ s 2 p le v e ls w h e n p a s s in g th r o u g h th e th i n s e c o n d fo il. A s a r e s u lt, a g r o w th is o b s e r v e d in th e d e c a y o f th e 5 .1 7 k e V lin e w ith s e p a r a tio n . In o r d e r t o d e te r m in e th e life tim e o f th e le v e l c o n tr ib u t in g t o th i s g r o w th , w e p e r f o r m e d a le a s t s q u a r e s fit u s in g th e e q u a ti o n
/ ( x ) = y ,e '" t + /2I l - e * " !
0
)th e o r e tic a l a p p r o a c h e s a r e 155 p s [2 0], 159 p s [2 1] and 157 p s [2 2 ]. T h is le v e l d e c a y s th r o u g h b o th autoionization as w e ll a s ra d ia tiv e p r o c e s s e s . T h e b r a n c h i n g ra tio for the a u to io n iz in g c h a n n e l is r a t h e r la r g e ( 6 3 % [2 0 ], 6 5 .7 % [2i}j T h e X - r a y c h a n n e l is a ls o s ig n if ic a n t (b r a n c h in g ratio 370/ [2 0 ] o r 3 4 .3 % [2 1 ] ). W e h a v e c a lc u la te d [1 8 ] th e energy of th e s a te llite lin e ls ^ 2 s \s 2 s 2 p *P%i2 in L i-lik e vanadium to b e 5 .1 4 2 k e V , a d if f e r e n c e o f o n ly 4 3 e V from the M2 Is^ 'S o - \ s 2 p ^ P \ l i n e in H e - lik e V a n d th u s can not be r e s o lv e d in th e X - r a y s p e c tr a b y o u r d e te c to r.
W e r e p e a te d th e a n a ly s is o f t h e s in g le - f o il d e c a y curve d iis tim e fittin g th e c u rv e w ith tw o , r a t h e r th a n o n e , exponents In th is p r o c e d u r e , th e lif e tim e o f th e s a te llite h a s been fixed to th e tw o -f o il v a lu e o f 125 ± 18 p s ( T a b le 1) a n d the error w a s re s tr ic te d w ith in 3cr to k e e p th e r e d u c e d close to u n ity . T h e life tim e o f th e \ s 2 p ^ P \ le v e l is d e te rm in e d in this m a n n e r a s 3 2 2 ± 2 8 p s ( T a b le 1). W e h a v e v e rifie d that the re la tiv e in te n s itie s o f th e m a in lin e a n d th e satellite line o b t a i n e d in t h e s i n g l e - a n d t h e t w o - f o i l e x p erim en ts c o r r o b o r a te w e ll ( T a b le 2 ).
Tabic 2. Comparison o f charge state fractions with line inten^iittes at
various beam energies from single* and two-foil data. I'he branching
ratios from [2 0 ) and [2 1 ] have been used to extract intensities from the
two-foil data.
H e re x is th e d is ta n c e b e tw e e n th e tw o fo ils . T h e life tim e o f th e d e c a y i n g le v e l, r i , w a s f ix e d to th e e ff e c tiv e v a lu e o b ta in e d fr o m th e s in g le fo il m e a s u r e m e n t. T h e life tim e r2 o f th e le v e l r e s p o n s ib l e f o r th e g r o w th a t 158 M e V is th u s d e te r m in e d to b e 125 ± 18 p s ( T a b le 1).
T h e \ s 2 s 2 p *P%a th e s e c o n d fo il in th e tw o -f o il fo r m o f th e e x p e r i m e n t m a y c o m e d o w n t o \ s 2 p ^ P \ f f e ith e r th e s t r ip p i n g o f 2 p e le c tr o n a s w e ll a s e x c ita tio n (2s -2p ) in a s in g le c o llis io n (2n d f o ils is th i n a n d it a llo w s o n ly o n e c o llis io n ) o r th e s t r ip p i n g o f 2 s e le c tr o n ( t h a t is v e i y v e ry u n li k e ly ) ta k e s p la c e . H o w e v e r d ir e c t e f f e c t o f t h e \s 2 s 2 p
*P%n io n s ( r e m a i n s u n a lt e r e d ) in th e s e c o n d f o il ( v e r y u n lik e ly a g a in ) c a n b e c o n s id e r e d w ith a n a d d itio n a l d e c a y c o m p o n e n t . O n t h e s e r e a s o n s th e e f f e c t o f th e \ s 2 s 2 p
*P%ri io n s f e e d i n g to l s 2 p ^ P \ is n o t a c c o u n t e d in th e e q u a tio n .
A t h o r o u g h s e a r c h o f v a n a d iu m le v e ls in v a r io u s io n ic s ta te s w a s th e n p e r f o r m e d , in a n e f f o r t t o id e n tif y th e le v e l w ith a lif e tim e o f 125 d: 18 p s t h a t is f u r th e r lin k e d to a lo w e r le v e l w ith a t r a n s it io n e n e r g y in th e v ic in ity o f 5 .1 7 k e V . T h is le v e l h a s b e e n id e n t if ie d a s t h e a u to io n iz in g \s 2 s 2 p *P%n L i- lik e V le v e l, f o r w h ic h th e lif e - tim e s p r e d ic te d b y d if f e r e n t
Beam Ratio o f Li-like Ratio o f satellite Ratio of satellite energy to Hc-like ion to main line to mam line (MeV) population [19] intensity
(single foil data)
intensity (two-foil data)
100 3.80 3.68 3.68 1201, 3 53 |21|
IS8 1.64 1.40 1.38 1201, 1 25 [2I|
A le a s t s q u a r e s f i t t o th e tw o - f o il d a ta a t 1 0 0 M e V using e q u a tio n (1) w ith ri f ix e d t o th e e ff e c tiv e s in g le foil value o f 161 p s ( T a b le 1), y ie ld e d a v a lu e o f 3 0 6 ± 3 2 p s for xi T h e r e la tiv e in te n s itie s o f th e 161 p s a n d 3 0 6 p s components fro m th e s e c o n d fo il w e r e 5 5 % a n d 4 5 % re s p e c tiv e ly . Using th is in te n s ity r a t io a n d f ix in g o n e c o m p o n e n t to 306 ps.
w e r e f itte d th e s in g le fo il d a ta w ith tw o e x p o n e n ts , keeping th e e r r o r w ith in 3 a a n d th e r e d u c e d d o s®
th u s d e te r m in e d a lif e tim e o f 1 2 1 ± 2 0 p s f o r th e second c o m p o n e n t. T h is im p lie s th a t, a t a b e a m e n e r g y o f 100 MeV.
th e X - r a y in te n s ity is d u e m a i n ly to th e s a te llite lin e and is f e d b y th e d e c a y o f H e - lik e tr a n s itio n . T h is c o n tra sts our fin d in g s a t 158 M e V a n d m a y b e e x p la i n e d b y re fe irin g to th e c h a r g e s ta te p o p u la tio n s ( 1 9 % L i- lik e a n d 5 % He-lik«) r e p o r te d in T a b le 2 . A t a lo w e r b e a m e n e r g y , \ s 2 p ^ P \ states m a y c tq ttu re a n e le c tr o n in d ie 2r o r b ita l w h ile pa.ssing th r o u g h th e s e c o n d fo il, t o g e n e r a te \ s2s2p * P}/2 levels and th u s e n h a n c e th e in te n s ity o f th e s a te llite lin e . W e als®
n o te th a t th e life tim e v a lu e s w ith t h e b e a m o f 1 0 0 M eV are
v e rv good a g r e e m e n t w ith th o s e o b ta i n e d f r o m th e a n a ly s is fthe 158 M e V d a ta .
The e x p e rim e n ta l lif e tim e s f o r \ s 2 p ^P%, d e te r m in e d in
„( w o rk b y ta k in g t h e b l e n d i n g d u e t o th e s a te llite in to ccount. a g r e e w e ll ( T a b le 1) w ith th e o r e ti c a l v a lu e s [ 17] a n d n! w ith h y p e rf in e q u e n c h e d lif e tim e e s tim a te s [1 ]. T h e jicllitc t o m a in lin e in te n s ity r a t io a ls o a g r e e s f a irly w e ll iih th e io n p o p u la tio n r a t io a t th e c o r r e s p o n d in g b e a m nerg) (T ab le 2 ). A s a f in a l s te p in o u r a n a ly s is , w e u s e d )c a b o v e re s u lts a n d f itte d th e s in g le fo il d a ta o f f2] (b e a m nerav 3 6 7 M e V ) w ith th r e e e x p o n e n ts . T h e m a in t o s a te llite nc i n t e n s i t y r a t i o w a s f i x e d t o t h e c o r r e s p o n d i n g io n o pulation ratio ( 2 6 .6 % L i- lik e a n d 5 6 % H e - lik e th r o u g h a 5 0 g em - c a r b o n fo il [ 1 9 ] ) a n d th e in te n s ity o f th e Ijt^ ' So-
\S'i line w a s f ix e d to th e m e a s u r e d v a lu e . T h e life tim e s f \s2p a n d \ s 2 s ^Sj w e r e a ls o f ix e d to 3 1 0 p s a n d 16.9 s r e s p e c tiv e ly . T h is p r o c e d u r e y ie ld s a v a lu e o f 173 ± 2 0 s t o r t h e \s 2 s 2 p *P%ri le v e l lif e tim e ( e r r o r w ith in 3 a ) w h ic h q u ite c l o s e to t h e o r e t i c a l e s t i m a t e s ( T a b l e 1). T h u s p p h c atio n o f o u r a n a ly s is to d a ta o b ta i n e d in a n e a r lie r udv (2] y i e l d s to o u r f i n d in g s . A v e r a g e o f th e life tim e s f o r
\ls2p'*P%2 o b ta in e d fr o m o u r a n d G o u ld e t a l d a ta [2 ] 21CCS q u i t e w e ll w ith th e e s tim a te s [2 0-2 2].
A lth o u g h th e p r e s e n t li f e t im e o f \ s 2 p ^ P \ d o e s n o t ccord w ith th e h y p e r f in e q u e n c h e d lif e tim e e s tim a te [ 1 ], w e avc tr ie d to fin d w h e th e r o u r d a ta c o n ta in s a n y e x p o n e n t f dl ps c o r r e s p o n d in g to th e \ s 2 p ^P%. It is s e e n th a t either o u r n o r G o u ld e t a l d a ta [ 2 ] a c c o m m o d a te s 91 p s
\p o n c n t. T h e r e f o r e , it im p lie s th a t f e e d i n g d u e t o h fs iduced B1 d e c a y to th e 5 .1 7 k e V lin e is n o m in a l. H o w e v e r , suitable h ig h r e s o lu ti o n m e a s u r e m e n t a s in [1 3 ] is p la n n e d re so lv e s a te llite a s w e ll a s h fs in d u c e d d e c a y o f th e 2/)-’ ^ 0 lev el.
To a v o id th e e f f e c t o f s a t e ll it e b l e n d i n g th e c r y s ta l pectrometer [1 4 ] a n d D o p p le r t u n e d s p e c t r o m e te r a re u s e d various m e a s u r e m e n ts . A n o th e r te c h n iq u e o f m e a s u r in g fetime o f le v e l th r o u g h E l b r a n c h [2 3 ] h a s a ls o b e e n u s e d , lie lifetim es o b ta in e d th r o u g h th e s e m e a s u r e m e n ts s h o w e d good a g r e e m e n t w ith th e th e o r e ti c a l e s tim a te s w ith o u t
•'ng the h y p e r f in e q u e n c h in g in to a c c o u n t [1 8 ] a s s h o w n Table 1. T h e e s t im a te fr o m th e G R A S P c o d e is v e r y isistent w ith [ 1 7 ] .
The life tim e f o r \s 2 s 2 p * P % a in L i- s e q u e n c e h a v e b e e n
^Iculated u s in g D ir a c - H a r t r e e - F o c k [2 0] a n d m a n y b o d y urbation, th e o r y w ith re la tiv is tic h y d r o g e n i c b a s is s e t The d a ta o b ta i n e d f r o m th e s e c a lc u la ti o n s c o r r o b o r a te with th e m o r e a c c u r a t e v a lu e s c a lc u la te d r e la tiv is tic a lly inter m e d i a te - c o u p li n g s c h e m e , u s in g D ira c - H a r tr e e - 'ater w a v e f u n c t i o n a n d t h e M d l l e r o p e r a t o r [ 2 2 ] .
Tabic 1. Comparison between theoretical estimates without taking the hyperfine quenching into account (GRASP) and experimental lifetime (ps) for \s2p^f^2 l«vc! o f some ions in lle-sequcnce where satellite was resolved.
Klcment Theoretical lixperimental
Ar 1480 1440 -i 80 |27j. 1620 ± 80 [23|
Ti 430 404 ± 40 (241
V 310 314 i- 30 |I 2 |
Cr t
-
4
- 227 215 35 |24|T h e p r e d ic te d life tim e s fo r \s 2 s 2 p * P \r i fo r v a rio u s L i-lik e io n s a re c o i^ p a r e d w ith in 2 0% w ith th e m e a s u re d v a lu e s as s h o w n in T ^ b le 2.
T h e m e a s u r e m e n ts w h ic h h a s n o t r e s o lv e d th e b le n d in g p ro b le m d u e to th e sa te llite , th e m e a s u re d life tim e o f 1 j2p “ is in fa c t a w e ig h te d a v e r a g e o f th e life tim e s o f \ s 2 p ^ P \ o a n d \s 2 s 2 p *P%n. w h e r e h y p e r f in e q u e n c h in g ta k e s p la c e . In th e a v e r a g e , th e re s p e c tiv e in te n s itie s p la y s th e m a j o r ro le . H e re , th e l.v^ 'Sq - 1s2 /j a n d l.v-2.v^.9|/2- \s 2 s 2 p *P%n a re M 2 w h e r e a s l.v^ 'iSq- \ s 2 p ^P% is h fs in d u c e d E l d e c a y a n d M 2 is p r o p o r tio n a l to Z* a n d h fs El p r o p o r tio n a l to Z*.
T h e r e f o r e , c o n tr ib u tio n o f 'S q - \ s 2 p ^P% in th e a v e ra g e c a n b e ig n o r e d fo r th e io n s h a v in g fin ite h fs. In a b s e n c e o f h fs , th e m e a s u re d life tim e o f \ s 2 p ^ P \ is s im p ly a w e ig h te d a v e r a g e o f th e li f e tim e s o f \ . s 2 p ^ P \ a n d Is2a'2/j
T h e re f o re , th e life tim e s o m e a s u re d m a y b e c a lle d a s th e e f f e c tiv e life tim e o f \ s 2 p ~^P\. It is th e w e ig h ta g e o f t h e life tim e s o f l.v2;> ^ P \ a n d \s 2 s 2 p ‘^P%a d e p e n d s o n th e c h a r g e s ta te fra c tio n o f H e - a n d L i-lik e io n s in th e fo il e x c ite d b e a m b e c a u s e v a rio u s c h a r g e s ta te s a re p r o d u c e d w h e n a n io n b e a m p a s s e s th r o u g h a fo il, th e b r a n c h in g ra tio s o f th e M 2 b ra n c h o f \ s 2 p ^ P \ a s it h a s a n o th e r b ra n c h o f E l d e c a y (1s2j - \ s 2 p ^ P \ ) a n d X - r a y (M 2 ) b ra n c h ( l . v W S x a -
\s 2 s 2 p * P % /2 ) o f \ s 2 s 2 p ‘'P % a a s it d e c a y a ls o th r o u g h e le c tro n e m is s io n (l.v ^ 'S q - \ s 2 s 2 p ‘^P%i{). T h e e f f e c tiv e life tim e o f \ s 2 p ^ P \ m a y b e w ritte n as
_ B R I X n 4- B R 2 X C F R x Tj
(
2
)B R 1 - I - B R 2 X C F R
w h e r e B R l is th e M 2 b r a n c h in g r a t io o f \ s 2 p ^ P \ , B R 2 th e X -ra y (M 2 ) b r a n c h in g ra tio o f \s 2 s 2 p *P%a s ta te a n d C F R th e c h a r g e d s ta te fr a c tio n r a tio o f L i- to H e - lik e io n s in th e fo il e x c ite d b e a m . T h is ra tio h a s b e e n o b ta in e d fr o m th e c o d e E T A C H A [1 9 ]. In th is e s tim a tio n , d a ta f o r th ic k n e s s o f th e c a rb o n fo ils , in c id e n t b e a m e n e r g y a n d th e c h a r g e s ta te a re ta k e n fro m th e p r e v i o u s m e a s u r e m e n ts ( T a b le 3 ).
T h is is v e r y c le a r fro m th e F ig u r e 1 th a t th e m e a s u r e d
\ s 2 p ^ P \ le v e l l i f e t im e , w h e r e s a t e l l i t e e f f e c t w a s n o t a c c o u n te d fo r, is lo w e r th a n th e th e o r e tic a l e s tim a te s fr o m tita n iu m t o c o p p e r a s th e th e o r e tic a l 1 s 2 s l p *P%a le v e l life tim e
412 T Nandi
(T a b le 2 ) is s m a lle r th a n th e th e o r e tic a l \ s 2 p lev el life tim e ( T a b le 1), W h e re a s th e tr e n d c h a n g e s in th e c a s e o f H e -lik e s ilv e r, h e re th e m e a s u r e d life tim e is h ig h e r th a n th e e s tim a te w ith o u t h y p e r f in e e f f e c ts b e c a u s e th e e s tim a te d m e a n life o f
\,s 2 s2 p ^ P% 2 is la r g e r th a n th e \ s 2 p ^ P \ lev el life tim e ( T a b le 3 ). In c id e n ta lly life tim e s o f th e \ s 2 p ^ P \ a n d \ s 2 s 2 p ^ P \ r i le v e l a r e m o r e o r le s s th e s a m e fo r k ry p to n a n d o b v io u s ly , m e a s u r e d d a ta [ 3 J a g r e e v e ry w e ll w ith th e e s tim a te s [ 1 7 ,1 8 ].
Table 2. Comparison between theoretical and experimental lifetime (ps) for \s2s2p^l*^y2 level of some ions in [j>scqucncc
Element Theoretical Experiments
Ar Ti V Cr
543 |2I), 563 120|
201 |2 l], 108 (20J 159 [21], 155 [20]
121 [20]
590 ± 18 [27]
236 ± 12 [24]
123 -t 20 [12]
140 JL 8 [24]
U n r e s o lv e d s a te llite lin e a lte r s th e \ s 2 p ^ P \ le v e l life tim e a n d m a n y a u th o r s [2] in te r p r e te d it as th e e ff e c t o f h y p e rf in e q u e n c h in g . In o r d e r to s h a d e s o m e lig h t o n it th e h y p e r f in e q u e n c h e d life tim e s a s e s tim a te d b y J a h n s o n e t a l \ \] a re p lo tte d in th e F ig u r e 1. H e re o n e fin d s th a t th e s e d a ta m a tc h q u ite w e ll w ith th e m e a s u r e d v a lu e s w h e r e s a te llite w a s n o t re s o lv e d in th e r e g io n Z < 3 6 , b u t s h o w e d la rg e d e v ia tio n fo r Z > 3 6 . T h is d e v ia tio n is a n a r tif a c t b e c a u s e o f s a te llite b le n d in g a s e x p la in e d a b o v e . T h e in te re s tin g fa c t is th a t s a te llite a f f e c te d m e a s u r e d life tim e s c o r r o b o r a te w e ll w ith th e e f f e c tiv e life tim e s a s o b ta in e d fro m th e e q u a tio n (1) (T a b le 3).
M e a s u r e d \ s 2 p ^ P \ le v e l life tim e (2 5 7 ± 5 p s) o f H c -Iik c V [2 ] w a s lo w e r th a n th e th e o r e tic a l e s tim a te s (3 1 0 p s). T h is o c c u r r e n c e w a s a t t r i b u t e d to t h e e f f e c t o f h y p e r f i n e q u e n c h i n g [2 ]. T h e ^*^^Ag47 h a s g o t a ls o f in ite n u c le a r m o m e n t a n d s p in a n d th e r e f o r e e x p e c te d to b e in f lu e n c e d b y h y p e r f in e q u e n c h in g to o to a s m a lle r life tim e [2 ]. B u t th e m e a s u re d \ s 2 p ^ P \ lev el life tim e o f 1.2 4 -t 11 p s [2 8 ] is la rg e r th a n th e th e o r e tic a l e s tim a te o f 1.08 p s w ith o u t h fs in to a c c o u n t . A l t h o u g h s a t e l l i t e b l e n d i n g p r o b l e m in t h i s
e x p e r im e n t [2 8 ] w a s n o t a t a ll m u c h b u t a s th e trend goes in F ig u r e 1, h y p e r f in e fie ld s e f f e c t w ill r e d u c e th e
10000
“ Theoty without hfs Satellite resolved Satellite unresolved Theory with hfs
Si.
1000
-\
\ \
\
100 \
\
15 20 25 30 35 40 45
Atomic number (Z)
50
Figure 5. Z v.v rZ are plotted to show the effect of satellite on (he
\s2p^P% level lifetime irrespective o f the hyperfine fields' dice!
life tim e in H e -lik e A g f u r th e r d o w n [ 1 ]. H o w e v e r, Johnson ct a ! h a v e s to p p e d th e c a lc u la tio n a t Z ~ 4 3 a n d thus the d r a m a t i c d i s a g r e e m e n t b e t w e e n t h e i r p r e d i c t i o n and e x p e rim e n ta l v a lu ^ c a n n o t b e , th o u g h v e ry o b v io u s as the tr e n d g o e s till z = 4 3 , q u a n tita tiv e ly c o m p a r e d . It is ver\
c le a r th a t G o u ld e t a l h a v e m e a s u r e d a n e f f e c tiv e lifetim e of |
\ s 2 p ^ P \ a n d \s 2 s 2 p ^ P % 2 c o m b in e d . M u c h lo w e r lifetime m e a s u r e d w a s c a u s e d b y th e f a c t th a t th e \$ 2 p ^P^2 life tim e is fa r fro m \ s 2 p ^ P \ le v e l life tim e . H o w e v e r, one can n o t ig n o re th e e f f e c t o f h y p e r f in e q u e n c h in g o n th e lifetime b u t to q u a n tif y it o th e r im p o r ta n t e f f e c ts m u s t b e taken into a c c o u n t. T h is w o rk e n s u r e s th a t th e h y p e r f in e quenching e f f e c t o n th e \ s 2 p ^ P \ le v e l life tim e is m u c h less than the e ff e c t in c u r re d o n th e e r r o r in tro d u c e d b y th e b le n d in g due
Table 3. Comparison o f effective lifetimes for l52p tcvcl in He-likc ions as obtained from the empirical formula and the mcasuremenis IhaJ suffered fVom satellite blending problem. Here v\ and BRI are estimated using GRASP and vi and BR2 from [21]. Foil thickness is given in pg/cin*
and positive charge state o f the beam g.
Element n
ps
ri ps
Beam MeV
Q Foil CFR BRI
%
BR2
% ps ps _
V 310 159 367 50 0.47 74 34 256 257 ± 5 [2]
V 310 159 158 12 35 1.64 74 34 256 243 ± 5 |12)
Fc 124.7 79 403 50 0.71 82 47 110 m . 5 i 5 |2|
Kr 9.53 9.5 700 34 200 0.51 89.8 76 9.52 9.5 ± .9 PI
Ag 1.08 1.4 3815 46 400 0.014 89.9 90 1.09 1.24 ± .iM ^
to the satellite lin e . T h e r e f o r e , th e p r e d ic tio n o n \ s 2 p ^ P \ level lifetim e in c l u d in g h y p e r f in e q u e n c h in g in to a c c o u n t [2 ]
certainly o v e r e s tim a te d . T h e r e is n o o th e r th e o r e tic a l calculations o n i s 2 p ^P% le v e l lif e tim e o f H e - lik e io n s w ith hyperfine q u e n c h in g in t o a c c o u n t. T h e o r e t ic a l c a lc u la tio n s jfe welcome in s e ttlin g th e m a tte r .
A new h fs in d u c e d E l c h a n n e l ( I s ^ 'Sq ~ l'*2p ^P%) in a Pgh re so lu tio n s p e c tr u m g iv e s a c le a r c u t e v id e n c e o f th e iffect o f h fs o n \ s 2 p ^P%. U s in g th i s fa c t, e f f e c t o f h f s o n
!,v2p V o is c o n f i r m e d in G d [? ]. B u t s u c h p o s s ib ilitie s d o lot appear fo r \ s 2 p ^ P \ , o n e n e e d s h e r e t o r e s o lv e h f s s p l it mes. T h e re fo re , in th e f ir s t s te p o n e w o u ld r e s o lv e th e ,aiellite in fin d in g th e e f f e c t o f h f s o n \ s 2 p ^ P %
We n o te th a t d ie f ir s t b e a m tw o - f o il s t u d y [3 ] s u g g e s ts hat the sh o rt liv e d H e - li k e K r \ s 2 p ^ P \ le v e l c o n v e r ts to th e ong lived l s2r \ 9 i le v e l w h ile p a s s in g th r o u g h th e s e c o n d oil (beam e n e rg y 7 0 0 M e V ). In th e a n a ly s is s a te llite w a s n o t onsidcred. O n e c o u l d a r g u e th a t I.v2s2p * P n2 s ta te in th e aiellitc c an c o m e d o w n t o UZs: a s w e ll b y a n e le c tr o n tripping o r a n e x c it a ti o n o f H e - lik e g r o u n d s ta te ( p r o d u c e d IV au to io n izatio n o f \ s 2 s 2 p ^ P n2 le v e l t o 1 ’Sq) to l s2.v
his im plies in te r a c tio n m e c h a n is m is c o m p e titiv e b e tw e e n he two p h e n o m e n a . O u r e a r l ie r r e s u lts [1 2 ] s u g g e s t th a t th e netastable a u to i o n iz i n g L i-lik e \ s 2 s 2 p * P i n le v e l (1 2 4 ± 19
is) plays th e m a j o r r o l e in r e - p o p u la t in g \ s 2 p ^ P \ a t th e cry thin s e c o n d fo il ( o n l y a c o ll is io n ta k e s p la c e ) a t 158 /IcV, w h e re a s th e r e v e r s e p r o c e s s { \ s 2 p ^ P \ c a p tu r e a n lectron in th e 2 s s h e l l t o p r o d u c e \ s2s2p * P n2 s t a t e ) ominates a t 100 M e V . T h is im p lie s in te r a c tio n m e c h a n is m
! highly d e p e n d e n t , th e w e ll k n o w n fa c t, o n p r o j e c ti le elocity. T h u s , t h e c u r r e n t s t u d y h in t s th e n e w p o s s ib ilitie s 1 elucidating th e m e c h a n is m o f in t e r a c t io n b e tw e e n e x c ite d tales anef a th i n fo il.
To s u m m a riz e , in th is s t u d y w e f itte d s i n g le f o il d a ta f o r le 5.17 k e V d e c a y in H e - li k e V w ith a s i n g le e x p o n e n t. T h e fetimes d e t e h n i n e d in th i s m a n n e r fr o m 1 0 0 M e V a n d 158 leV ion b e a m s d i f f e r c o n s i d e r a b l y d u e to b le n d in g . T h e se o f th e tw o - f o il ta r g e t v a r i a n t o f th e b e a m - f o il tim e - o f - ight te c h n iq u e a n d s u b s e q u e n t f itt in g o f th e s in g le fo il 3ia w ith t w o e x p o n e n t s h a v e m a d e p o s s i b l e t h e rterraination o f th e lif e tim e s o f b o th th e m a in a s w e ll a s th e
•icllite lin e th a t c o n tr ib u t e t o t h e 5 .1 7 k e V d e c a y . T h e ''^rage life tim e ( 1 2 3 ± 19 p s ) f o r th e I s 2 s 2 p * P s n *®vel is onsi.stent w ith th e o r e ti c a l e s t im a te s [ 2 0 - 2 2 ] . T h e a v e r a g e
"lie fo r th e \ s 2 p ^P% le v e l a t tw o v e lo c itie s h a s b e e n luced to b e 3 1 4 3 0 p s . T h is v a lu e is s u p p o s e d t o a g r e e '•*1 the h y p e r f in e q u e n c h e d lif e tim e o f 2 4 2 p s [1] b u t it is lose to t h e o r e t i c a l e s t i m a t e s , o b t a i n e d w i t h o u t ta k i n g yperfine f ie ld s in to a c c o u n t. T h e r e s u lt t h u s c o n f i r m s th a t
th e e ff e c t o f h y p e r f in e q u e n c h in g is n o t s i g n if i c a n t f o r th is le v e l w ith in th e e x p e r im e n ta l u n c e r ta in tie s w h ic h in tu r n i m p l i e s th e s h o r t c o m i n g o f t h e m e t h o d s u s e d in t h e c a lc u la tio n s [ 1 ] a n d th e r e f o r e , f u r th e r th e o r e tic a l c a lc u la tio n s a re c e r ta in ty r e q u ir e d to c o n v e r g e th e d is c r e p a n c y b e tw e e n th e e x p e riik ie n t a n d th e th e o r ie s .
i
O u r r ^ u l t s f u r t h e r s u g g e s t t h a t t h e m e t a s t a b l e a u to io n iz in jg L i-Iik e 1 s 2 s 2 p le v e l (1 2 3 19 p s ) p la y s th e m a j o r r o le ||n r e - p o p u la t in g \ s 2 p at th e s e c o n d fo il a t 158 M e V , w h e r e a s th e re v e r s e p r o c e s s d o m in a te s a t 1 0 0 M e V . O u r f in d in g s c o n firm th a t th e u s e o f a tw o - f o il ta r g e t p r o v id e s th e m e a n s f o r s tu d y in g th e in te ra c tio n m e c h a n is m o f e x c ite d s ta te s w ith a fo il. W e n o te th a t th e firs t b e a m tw o - f o il s tu d y [3 ] s u g g e s ts th a t th e s h o r t liv e d H e - lik e K r \ s 2 p ^ P \ le v e l c o n v e r t s to th e lo n g liv e d 1j2j \ S | le v e l w h ile p a s s in g th r o u g h th e s e c o n d fo il (b e a m e n e r g y 7 0 0 M e V ). T h e p re s e n t s tu d y in d ic a te s a d if f e r e n t p r o c e s s d o m in a tin g in v a n a d iu m in th e e n e r g y r a n g e 2 - 3 .1 M e V /U . T h u s , th e a p p r o a c h f o llo w e d in th e c u r r e n t s tu d y o p e n s u p n e w p o s s ib ilitie s in s p e c tr o s c o p ic s tu d ie s in h ig h ly c h a r g e d io n s a n d a s s is ts in e lu c id a tin g th e m e c h a n is m o f in te ra c tio n b e tw e e n e x c ite d s ta te s a n d a th in fo il.
O u r sim p le im p iric a l fo rm u la c o n f in n e d th a t s a te llite a fib e ts s u b s ta n tia lly th e life tim e o f l5 2 p ^ P \ le v e l i f it is n o t r e s o lv e d in th e e x p e r im e n t. T h e h y p e r f in e in te ra c tio n q u e n c h e s th e
\ s 2 p V 2 le v e l ie te tim e b y m o r e th a n 5 % [2,1 ] is u n d o u b te d ly f o r tu to u s , th e r e f o r e , r e lia b le c a lc u la tio n s a re h ig h ly re q u ire d . F u r th e r , th is s tu d y w a r r a n ts th e re s u lts w h e r e b le n d in g e f f e c t w a s n o t t a k e n in t o a c c o u n t a n d u n f o r t u n a t e l y d r e w d e n g e r o u s c o n c l u s i o n s . T h u s o u r s t u d y s g g e s t s t h e e x p e r im e n ts a ff e c te d b y b le n d in g m u s t b e r e p e a te d . T h e life tim e s o f tw o - a n d th r e e - e le c tr o n io n s a re r e l e v a n t in c o n n e c tio n to a s tr o p h y s ic s [3 0 ], la s e r - in d u c e d p la s m a s [3 1 ] a n d th e p h y s ic s o f a to m ic c o llis io n [3 ]. H o w e v e r, o n e o u g h t to b e n o w c a re f u ll b e f o r e u tiliz in g s u c h lif e tim e s in a n y a p p lic a tio n s .
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