state  is mixed with  the  2‑P1 state which can  decay rapid1y  to the l

11S0  ground  state.  Two measurements of  the quenching dccny 

. . 1 3 )  

rate have been reported.  Petrasso and 

Ramsey~-'

measured  the attenuation of  a metastab'e beam passing between para11cl  e1ectric‑fie1d p1ates and 

Johnson-~' 14) 

emp10yed a time

^目

of‑

f1ight technique  to measure direct1y  the  1ifetime of 2 1 5 0  state atoms passing  through an e1ectric  fie1d. 

The  fie1d‑induced decay rate is proportiona1  to E 2 ，  where  E is the e1ectric‑fie1d  strength.  The aim of experimental  and  theoretica1 effort

弓

is to determine the propor

七

ionality

factor ，  C‑ 1 .  Thus  it is  seen that the  1ifetime τis given by 

︐ 

︑ よ

l 

q4 

E 

戸﹂

+ 

︑ よ

) ) 

nu  

{ 

t 

l  i 

‑ ‑

} 

E 

( 

Th 

where τ(0)  is  the 1ifetim

己

of the 

2-S~

l  stnte  in  zero fie1d. 

O 

The resu1ts are shown together with theoretica1 

va1ues  in A‑4a‑Table  4 .   It i5 

SE:

en that  the experiment.u  values are in good agreement with each o t . her as we11 as 

¥'II七

h the theoretica1  ¥a1ues.  The 1ifetimeτ(E)  i5 show

"I1 

as 

r.̲̲ ，...

‑1 ̲ 

I'\~ ^'1

̲ . . . 2 1 ̲  ̲  ̲̲2  a function of E in A‑4a‑Fig.  2

ム

or C ‑ .93  kV‑js'cm‑. 

‑Ra.A4‑6‑

Survey of Calculations

The factor proportional to the quenching decay rate, C , has been calculated accurately by Petrasso and Ramsey,

Drake

1 5 )

and Jacobs,

16

* although

deta

ils of the latter results have not been published. Petrasso and Ramsey based their calculation on known' oscillator strength, while Drake employed a time-independent perturbation theory approach. The results are given in

A-4a-Table 4. It j? seen that the very precise values obtained theoretically by Drake and experimentally by

Johnson are also in excellent agreement. 141

Unperturbed Lifetime of the 2 S. ._ State of He

+ s

l/2

Survey of Experiments

The only measurements that have been reported

for the field-free lifetime of the 2 S. ,

2

state of He

+

are those of Prior

17

* and of Kocher et al.

1 8

* Prior

used a Penning-type electromagnetic trap to store, for periods of 8 ms. ions produced by a pulse of electrons

2 passing through He gas. Those ions in the 2 S,

/ 2

state decayed by two-photon emission and the number of emitted photons

w a s

then measured as a function of the time after excitation. Corrections to the lifetime obtained from the slope of the decay curve were made for collisional quenching and for field quenching. Kocher et ai. measured

-Ra-A4-7-Survey of Calculations 

The factor proportiona1  to the quenching decay rate ，  C‑ 1 ，  has  been calculated accurately by Petrasso and Ramsey ， 

13) 

Drake15) and Jacobs ， 16)  altnoughdetai1s of the latter  results have not been published.  Petrasso and Ramsey  based their calculation on known' oscillator strength ， 

while Drake emp10yed  a time‑independent perturbation  theory approach.  The  results are given  in A‑4a‑

Tab1e 4 .   It 

jp 

seen  that  the very precise values obtained  theoretically by Drake and experimenta11y by 

Johnson-~I

14)  are a1so in exce11ent agreement. 

Unperturbed Lifetime of the  22s ，  ，~ State of He+ 

1/2 

3urvey of Experiments 

The on1y measurements that have been reported 

2̲ 

+ 

for  the fie1d‑free 1ifetime of the 2‑S. 

I~

state of He'  are  1/2 

，

17)  ̲ ̲ ‑ "  

̲&:  v_~ }-，~~ ̲.. 

  ， ̲ 18) 

those of  prior‑"  and of  Kocher et  a1.‑

^{u 1}  

Prior  used a penning‑type e1ectromagnetic trap to store ， ^for 

periods of 8 m 7 ions produced by a pu1se of e1ectrons  passing through He gas.  Those  ions  in the 22s 

1/2  state decayed by t . wo‑photon emission and the nnmber of  emitted photons was  then measured as a function of the  time after 

e~citation.

Corrections to the  1ifetime obtained  from the  slope of the decay curve were made for co11isiona1  quenching and for  fie1d quenching.  Kocher et a1.  measured 

‑Ra‑A4‑7‑

the in-flight decay of metastable ions produced by electron bombardment of helium gas. The ion beam was accelerated to 200 eV and then it travelled down tii 8-m drift tube in which the intensity of the 2 S

1

,

2

i °

n s

w a s

measured using a travelling detector. One main

contribution to the uncertainty, in this measurement is

due to de-excitation of the metastable ions by residual gases including a vapor with a large quenching cross section.

The results of these experiments are shown in A-4a-Table 5. Although, the valuas are in fair agreement, the experimental uncertainty is rather large, especially for the measurement of Kocher et al. However, both values agree within experimental error to the very closely agreeing and precise theoretical values.

The energy distribution calculated theoretically

by Spitzer and Greenstein, Klarsfeld ana Johnson for two-photon decay of the 2 S, ,~ state has been verified by Artura et al. However, the results, 19) obtained using a broadband spectroscopic coincidence counting thechnique with the frequency selection

determined by the transmission of various filters, are integrated over large frequency bands, and are

relativs values. Therefore, from these results it is not possible to obtain the number of photons emitted

per unit time at a given energy.

-Ra-A4-8-the in

司

f1ight decay of metastab1e  ions produced by  e1ectron bombardment of he1ium gas.  The ion beam was  acce1erated to  200 eV and then it  trave11ed down 

ι~l

8‑m  drift tube  in which the  intensity of the  22S1/2  ions  was  measured using a trave11ing detector.  One main  contribution to the uncertainty. in  this measurement  is 

due to de‑excitation of the metastable  ions by residual gases  including a vapor with a 1arge quenching cross section. 

The results of these experiments  are shown  in A

^皿

4a‑

Table  5.  A1though ，  the 

va1u~s

are  in  fair agreement ， 

the experimenta1 uncertainty i5 rather  large ，  especially  for  the measurement of Kocher et a1.  However ，  both  va1ues agree within experimenta1 error to the very  c1ose1y agreeing and precise theoretical va1ues. 

The energy distribution ca1cu1ated theoretica11y 

2 1   ) ，   . . .

___~_， ....24)

̲̲̲ 

T~...____25)

by Spitzer and Greenstein ， . ‑ '   K1arsfe1d‑"  ana Johnson  for two‑photon decay of the  2‑S 2  1/2  state has been  verified by Artu 日 主 主 主 と

19) 

However ，  the resu1ts ， 

obtained using a broadband spectroscopic coincidence  counting thechnique with the frequency  se1ection 

determined by the transmission of various  fi1ters ，  are  integrated over 1arge frequency bands ，  and are 

r e 1 a t i v : : !   va1ucs. 

'l'herefort~ ，

f r o r : 1   these resu1ts  it is not  possibh' to obtain the number of photons emi  tted 

pcr unit time at a given energy. 

‑Ra‑A4

^・

8‑

Survey of Calculations

2 •*•

The 2 S,y

2

metastable state of He decays predominantly by two-photon (2E1) emission. Calculations of the

transition rate for two-photon emission by an unperturbed H(2 Sj,

2

) atom have been reported by Breit and Teller, Spitzer and Greenstein, Shapiro and nroit, Zon and Rapoport and Klarsfeld. Since, t.hc; transition rate is proportional to Z and radiative corrections are negligible at low Z, the fiolcl-frne lifetime of the 2

2

S ,

/ 2

state of He

+

is

T

H e

+

'

=

Using the values of the hydrogen transition probability, A,,, reported by these authors, He (2 S-

/ o

) transition rate and lifetime values have been calculated and the results are listed in A-4a-?ablo '.>. In addition, Johnson has reported direct calculations of tho transition rate

for the 2 S . ^ state of He , which a m given in the same table. All the calculations arc baned on second-order perturbation theory withvarious degrees of precision, the most precise being that of Klarsfulri, in which the summation over the intermediate states was performed exactly

in closed form non-relativisticalLy, and that of Johnson who performed a relativistic calculation.

All the calculations are in excellent agreement with each other, with the difference between the

-Ra-A4-9-Survey of Ca1cu1ations 

The 22sl/2metastable state Of l l e   decays prodominantly 

^d 

by two‑photon  ( 2 E 1 )   emission.  C e I J . c u 1 a t : ions 0

王

the

t

J:'

ansi  tion rate  for  t ¥

oJ

o‑phot.on  emj.s"ion  by an unperturbed 

H(2~S1/2)

atom have been reporte(t  hy Breit and Te11er ，  20)  2 1 )  

ー・ ...̲̲:.. 

22) 

Spitzer and Greenstein ， ‑ . '   Shapiro e l n d  

nr ，~it ，--'

Zon and  2 3 )  

~_-'l v ， ~_c"ç~ ，-'l

2 4 )  

C

・

Rapoport-~'

and  K1arsfe1d. ̲ . "   . r i u c ( ¥   t . h e   t . r

孔

11sition ra  te  is proportiona1 to Z  6 

^U 

a n c l   l ' a c ! i i l  ti vc 

C'

on'ections  are neg1igib1e at 10w Z ，  the fin1d‑frn

p. 

1ifetin¥e  of the 22s.  ，~ state of He  +  is 

112 

TH\~+

( ' 白

︑

4

‑ E  E 

A 

r o  

昭白

H 

T 

Using the va1ues 0 王 the hydrogen t : r n n s i 七 . i on probabi1ity ， 

AH ，  reported by these authors ，  He  ( : ! 2  ‑ S

斗

/2) transH

ニ

ion rate and  1ifetiml1  va1ues have b e e l l   ca 二 ell1ated and the  resu1 ts are 1  isted in A‑4a‑7ab1e ! i .   ln addi  t i O l l ，  Johnson  /5)  has reported direct ca1cu1ations ( > f

七

he tl'ansition rate 

」 占 +

for the 2‑S1/2 state of He' ，  which

礼

r

p.

given in the same  table.  A11 the ca1cu1a tions are h a ! ， ^{e c 1}   on second‑order  perturbation theory withvarious 

d~grees

of precision ，  the  mos

七

precisebeing that 0 王 K1arsfu1d ， in which the sununation  over the intermediate states 

¥oIdS Jlel~f():r""ed

exactly 

in c10sed f o r r n   non‑re1ativisticaL

，

y .   i t n d   that of  Johnson who perforrned a 

re1ativis~ニ ic

ca1cu1ation. 

A11 the ca1cu1ations are in exce1 二 en

七

ag r . eernent with each other ，  with the differellc ・ between the 

‑R a ‑ A4

，

9‑

extreme values being less than 0.03% as can be seen

in A-4a-Table 5. In view of the firm basis of the theory, these values are expected to he very accurate. Spitzer and Greenstein, Klarsfeld and Johnson have

calculated the energy distribution of the photons emitted in the two-photon decay of the 2 S, ,_ state of atomic hydrogen Since the relative energy distribution of the emitted

2

photons is expected to identical for the 2 S. .^ states of both H and He , these relative values are

given in A-4a-Table 6. Again, the agreement

is very good. The values of Klarsfeld and Johnson, which are identical, are plotted in A-4a-Fig.3 Lifetime of the 2 S, ,~ State of He in an Electric -Field

Theoretical Result

26}

Lamb and Skinner

t

have calculated the lifetime of the 2 S, ,, state of He in an electric field on the basis of Stark mixing between this state

and the 2 P1/5

st

ate. The perturbed lifetime as a function of the electric field, E, can be conveniently expressed as

T ( E )

=

[ ( T ( O ) ) "1

+ 62.5E

2

]"

1

s,

2

for low fields where T ( 0 ) is the lifetime of the 2 S, ,_ state in zero field and E is in V/cm. A plot of T(E) as a function of E is shown in A-4a-Fig.4.for a more accurate but

non-ana ly tic theory.

-RaA4-10-extreme va1ues being  1ess  than  0.03%  as can be seen 

in A

・

4a‑Tab1e 5 .   In view of the  firm basis of  the  theory ， 

these va1ues are expected to he very accurate.  Spitzer 

i ょ)~， ___r_ ， ~24) __~

T̲L̲̲̲̲25)  and 

Greenstein ， ~./K1arsfe1d~~1

and 

Johnson-~I

have 

ca1cu1ated the energy distribution  of the photons emitted  in the two‑photon decay of the  2‑S 2  1 / 2  state of atomic hydrogen  Since the re1

苧

tive energy distribution of the emitted 

photons  is  expecte!d  to  identicu1  for  the  2 2

S 1 /2 states  of both H and He+ ，  these re1ative va1ues are 

given in A‑4a‑Tab1e  6 .  

l¥

gain ，  the agrecmcn t .  

1s very good.  The va1ues of  I < . la

l."

sfe1d and Johnson ， 

which are identica1 ，  are p10tted  1n A‑4a‑Fig.3  L  ̲    ̲ ̲ + 

Lifetime of the  2‑S.  1/2 

，~

State of He'  in  an E1ectric 

~ie1d

τneoretica1  Resu1t 

Lamb and Skinner‑‑' have ca1cu1ated the 1ifetime 

26) 

L 

+ 

of the  2‑S. 

，~

state of He'  in an e1ectric  fie1d  1/2 

on the basis of Stark mixing between  this stote 

and the 22p ₁ ， 

_{/ 2 ・}

I~ state.  The perturbed  1ifetime as a function 

_r

of the e1ectric  fie1d ，  E ，  can be convenient1y expressed as 

︐ 

S 

14

q4 

‑

rコ

E 

q4 

l 

 

rb

+ 

 

可よ

} } 

n u 

( T ( [ 

一 一

) 

E 

( 

ヤL

for  10w fie1ds where 

T(O) 

is  the 1ifetime of the  22S ，.~ _1/2  ^state  in zero fie1d and E is  in V/cm.  A p10t ofτ(E)  as a 

~unction

of E is shown in A‑4a‑Fig.4. for a more accur

司

te but non‑

ana1y tic  theory. 

‑Ra‑A4

・

10‑

4 2

Lifetimes of the P and P Autoionizing States of He

The reader is referred to section A-2b, in which the lifetimes of all the autoionizing states are considered.

(W. Shearer-Izumi, November 24, 1976)

-Ra-A4-11-4̲  "2̲ ̲ .  ̲ 

^{. 四}

Lifetimes of  the 

~p

and 

~p

Autoionizing States of  He 

The reader  is  reIcrred  to section A‑2b ，  in which  the  1ifetimes  of  all  the autoionizing  states are  considered. 

(W.  Shearer‑Izumi ，  November  24 ，  1976) 

‑Ra.A4.11‑

References

1) H.W.Moos and J.R.Woodworth: Phys. Rev. Lett. 3_0_, 775 (1973).

2) J.R.Woodworth and H.W.Moos: Phys. Rev. A 12_, 2455 (1975) . 3) O.Bely and P.Faucher: Astron. Astrophys. 1_, 37 (1969) . 4) G.W.P.Drake, G.A.Victor and A.h.Dalgarno: Phys. Rev. 180,

25 (.1969) .

5) G.W.F.Drake: Phys. Rev. A 3_, 908 (1971) .

6) G.Feinberg and J.Sucher: Phys. Rev. Lett. £6_, 681 (1971).

7) A.S.Pearl: Phys. Rev. Lett. 2£, 703 (1970).

8) R.S.Van Dyck,Jr.,C.E.Johnson and H.A.Shugart: Phys. Rev. Lett.

.2_5, 1403 (1970).

9) R.S.Van Dyck,Jr., C.E.Johnson and H.A.Shugart: Phys. Rev. A4_, 1327 (1971).

10) h, Dalgarno: Monthly Notices Roy. Astron. Soc. 131, 311 (1966).

11) G.A.Victor: Proc. Phys. Soc. 9_1, 825 (1967).

12) V. Jacobs: Phys. Rev. A4_, 939 (1971).

13) R. Petrasso and A.T.Ramsey: Phys. Rev. A5_, 79 (1972) . 14) C.E.Johnson: Phys. Rev. A7_, 872 (1973).

15) G.W.F.Drake: Can. J. Phys. 5jO

r

1896 (1972).

16) V. Jacobs: reported in ref. (14).

17) M.H.Prior: Phys. Rev. Lett. 2£, 611 (1972) .

18) C.A.Kocher, J.E.Clendenin and R.Novick: Phys. Rev. Lett.

2J3, 615 (1972).

19) C.J.Artura, N. Tolk and R.Novick: Astrophys. J. 3 S7,L181 (1969).

20) G. Breit and E. Teller: Astrophys. J. 9_1, 215 (1940).

-Ra-A4-12-References 

1 )   H . ¥ ' l . H o o s   and J.R.t

¥l

oodworth:  Phys.  Rev.  Lett. 

~旦，

775  (1973). 

2 )  

J.R.~voodworth

and H.¥v.Hoos:  Phys.  Rcv.  A 12 ，  2455  (1975). 

3 )   O.se1y and P.Faucher:  Astron.  Astrophys.    ， ! 37  (1969). 

4 )   G.W.P.Drake ，  G.A.Victor and A.l ， .Da1garno:  Phys.  Rev. 辺 旦 ，

25 

(1

969). 

5 )   G.W.F.Drake:  Phys.  Rev.  A 3

，リ

O B (1971). 

6 )   G.peinberg and J.Sucher:  Phys.  Rev.  Lett.  26 ， 

1)

81  (1971). 

7~

A.S.Pearl:  Phys.  Rev.  Lett.  ! ! ，   703  (1970). 

8 )   R.S.Van Dyck ， Jr. ， C.E.Johnson and H.A.Shugart:  Phys.  Rev.  Lett. 

25 ，  1403  (1970). 

9 )   R.S.Van Dyck ， Jr. ，  C.E.Johnson and H.A.Shugart:  Phys.  Rev.  A! ， 

1327  (1971). 

10) ム. Da1garno:  Month1y Notices Roy.  Astron.  Soc.  131 ，  311  (1966). 

11)  G.A.Victor:  Proc.  Phys.  Soc.  91 ，  825  (1967). 

12)  V.  Jacobs:  Phys.  Rev.  A 主 ， 939  (1971). 

13)  R.Petrasso and A.T.Ramsey:  Phys.  Rev.  . 1 1 ， . . ? ，   79  (1972). 

14)  C.E.Johnson:  Phys.  Rev.  A7 ，  872  (1973). 

15)  G.W.F.Drake:  Can.  J.  Phys.  5 ， 旦 1896  (1972). 

16)  V.  Jacobs:  reported in ref.  (14). 

17)  M.H.Prior:  Phys.  Rev.  Lett.  29 ，  611  (1972). 

18)  C.A.Kocher ，  J.E.C1endenin and R.Novick:  Phys.  Rev.  Lett. 

20)  G .   Breit and E.  Te11er:  Astrophys.  J. 

~，

215  (1940). 

‑Ra‑A4‑12‑

21) L. S p i t z e r , J r . , and J . L . G r e e n s t e i n : A s t r o p h y s . j , 1 1 4 , 407 ( 1 9 5 1 ) .

22) J. S h a p i r o and G. B r e i t : P h y s . R e v . 1 1 3 , 179 ( 1 9 5 9 ) . 23) B . A . Z o n and L . P . R a p o p o r t : J E T P L e t t . 7_ , 52 ( 1 9 6 8 ) .

!>4) S. K l a r s f e l d : P h y s . L e t t . 30A, 3 S 2 (1969) . 25) W . R . J o h n s o n : P h y s . R e v . L e t t . 2_9,1123 ( 1 9 7 2 ) .

26) W . E . L a m b , J r . . a n d M . S k i n n e r : P h y s . R e v . 7 8 , 539 (1950)

-Ra-A4-13-21)  L .   Spitzer ，  Jr. ，  and J.L.Greenstein:Astrophys . J.  114 ， 

407  (1951). 

22)  J .   Shapiro and G.  Breit:  Phys.  Rcv. 斗 l ， 179  (1959). 

23)  B.A.Zon and L.P.Rapoport:  JETP Lctt. 

~t

S2  (1968). 

24)  S.  K1arsfe1d:  Phys.  Lett. 旦 主 ， 382  (1969). 

25)  W.R.Johnson:  Phys.  Rev.  Lett.  29 ， 1123  (1972). 

26)  vl.E.Lamb ，  Jr. 

i'l

nd M.  Skinner:  Phys.  Rev.  78 ，  539  (1950). 

‑Ra‑A4

・

13‑

Ra-A4-Table 1. Results of measurements for the lifetimes of the metastable states of neutral helium.

State Lifetime Method Reference

2

3

S. 9090 s ± 30% Brightness decay (2)

2

1

S

Q 3 S

.,

8 m s

In-flight decay (7)

2

1

s 19-7 i 1-0 ms " " (9)

-Ra-A4-14-S t a ' : :

コ，

2 3 S  l  2 1 S 

O  2 1 S  。

Ra‑A4

・

T a b l e 1 .   Resul ts  of measurements for the  lifetimes  of the metastable states  of neutral  helium. 

Lifetime  Method  Reference 

9090  s

:t 

30

も

srightness decay  ( 2 )  

38 ョ B ms  In‑flight c i ( ' c a y   ( 7 )   19.7  1  1 .   0 ms  "  "  ^{( 9 )}  

•

‑Ra‑A4‑14‑

I

30

a

i

5t

Ra-A4-Table 2. Theoretical results for the transition rates important in the determination of the neutral-helium metastabio-state lifetimes and the corresponding lifetime values.

Transition Transition Lifetime Transition Type

Method Reference

2 \ 2E1

2E1 Ml Ml 2E1 2E1 2E1 2E1 2E1

3.47 x 10 4.02 x 10 0.000127 0.00012

46 50 51.3

50.89

b

"

9

~

9

ドキュメント内 1976$ (ページ 139-148)