VOLUME 30, N U M B E R 9 P H Y S I C A L R E V I E W L E T T E R S 26 FEBRUARY 1973

eter-dependent cross section for Coulomb K-shell ionization by slow particles is confirmed in detail with protons by coincidence measurements between the emerging scattered particles and the characteristic target K-shell x rays emitted in the process of filling the K -shell hole created by the penetrating particle. This provides a well-documented basis for the quantitative search of impact-parameter-dependent deviations that must occur when Z1 — Z2 and Pauli excitation of the K shell becomes dominant.

One of us (WJB.) had the benefit of discussions with G. Basbas, L. C. Feldman, and R. Laubert.

*Work per formed under the auspices of the U. So Atomic Energy Commiss ion .

t P e r m a n e n t a d d r e s s : Depar tment of Phys ics , New York Universi ty, New York, N. Y. 10003.

1W. Brandt , in Proceedings of the International Con­ference on Inner-She 11 Ionization Phenomena, Atlanta, Georgia, April 1972, edited by R. W. Fink, S. T. Man-son, M. P a l m s , and P . V. Rao (U. S. Atomic Energy Commiss ion, Oak Ridge, Tenn. , 1973), p . 948.

2 E. Laegsgaard , J . V. Andersen, and L. C. Feldman, in Proceedings of the International Conference on Inner-Shell Ionization Phenomena, Atlanta, Georgia, 1972, edited by R. W. Fink et aL (U. S. Atomic Energy Com­miss ion , Oak Ridge, Tenn. , 1973), and Phys . Rev. Lett .

29, 1206 (1972). 3 J . Gang and J . M. Hansteen, Kgl. Dan. Vidensk.

Selsk., M a t . - F y s . Medd. ,31, No. 13 (1959). 4W. Brandt and R. Lauber t , Phys . Rev. Let t . £4, 1037

(1970). 5W. Brandt , in Proceedings of the Third International

Conference on Atomic Phys i c s , Boulder Colorado, Au­gust 1972, edited by S. J , Smith (Plenum, New York, to be published),

6M. Bara t and W. Lichten, Phys . Rev. A <3, 211 (1972). 7 F . P . Lark ins , J . Phys . B: P r o c . Phys . S o c , Lon­

don 5, 571 (1972). 8G. Basbas , W. Brandt , and R. Laubert , Phys . Rev.

A (to be published). 9H. Jo Stein, H. O. Lutz, P . H. Mokler, K. Sis temich,

and P . A r m b r u s t e r , Phys . Rev. Let t . 24, 701 (1970), and Phys . Rev. A 2, 2575 (1970), and 5, 2126 (1972).

10Integration of Eq. (3.12), Ref. 3, over final s t a tes Ef. n T . Huus, J . H. B j e r r e g a a r d , and B. Elbek, Kgl. Dan.

Vidensk. Selsk., M a t . - F y s . Medd. 30, No. 13 (1956). 12W. Brandt , R. Laubert , and I. Sellin, Phys . Let t .

2J., 518 (1966), and Phys . Rev. 151, 56 (1966). 13Note that integrat ion of Eq. (2) with P(cx) y ie lds a

cor rec t ion factor for Coulomb deflection, G(q0d)-2TT x /0°°P(cx)x dx = 2TT/2* d P(x')(x' -qod) dx'9 to the c r o s s sect ion (JK(£,K), Eq. (3). It r e p r e s e n t s a " s t r a igh t - l i ne" approximation, and becomes essent ia l ly equal to the factor 9£10(7rg0d) for a hyperbolic t ra jec tory as der ived e a r l i e r (Ref. 12) if one se t s G(q0yd) with y ~ir in our range of x va lues .

Photomagnetic Positronium-Spin Conversion in Solids*

Werner Brandt and Paul Kliauga Department of Physics, New York University, New York, New York 10003

(Received 12 December 1972)

We have observed spin convers ion of or thoposi t ronium and parapos i t ron ium in i n t e r a c ­tion with photoexcited, me tas t ab le , paramagnet ic t r ip le t s ta tes of phosphorescent m o l e ­cules in r igid solut ions , through changes in the posi t ron lifetime s p e c t r a induced by light. The r e s u l t s bea r on the s t a t i s t i c s of the spin convers ion p r o c e s s e s , and on the dif­fusion of posi t ronium in so l ids .

Phosphorescence of organic molecules in solid solutions is attributed to the slow (relative to fluorescence) emission of light in symmetry-for­bidden transitions from the lowest paramagnetic triplet state T (spin quantum number S= 1) to the diamagnetic singlet ground state (S = 0).1,2 Photo-magnetism was first demonstrated in the pioneer­ing work of Lewis, Calvin, and Kasha3 through measurements of the magnetic susceptibility of phosphorescent solids under illumination, Since then, the properties of molecular triplet states have been investigated extensively by electron-spin resonance and in the framework of exciton physics.4

We report first observations of the photomag­netic spin conversion of orthopositronium o-Ps (electron and positron spins parallel, S= 1) and of parapositronium p-Ps (electron and positron spins antiparallel, 3=0) in interaction with mole­cules in photoexcited triplet states, imbedded in rigid diamagnetic matrices. Our results open the possibility for measurements of the spin-statistic probabilities of ortho-to-para and of para-to-ortho positronium conversion. More­over because of its monotonic dependence on the light intensity, spin conversion provides a flexi­ble new method for the study of Ps propagation in solids through the interaction with conversion

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VOLUME 30, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 26 FEBRUARY 1973

s i t e s of continuously var iab le s t eady-s t a t e con­centra t ion.

Conceptually the exper iment is s t ra ight forward . Light of wave number D and intensity I0(v) e n t e r s , at x = 0, a solid s lab of th ickness D of a t r a n s p a r ­ent solvent of molecu la r density n, containing phosphorescent molecu les at the concentrat ion c. At the depth x, the light p roduces a s t eady-s t a t e concentrat ion cT{x,D) of randomly dis t r ibuted t r ip le t - exc i t ed molecu les T. In the validity range of L a m b e r t - B e e r ' s law,

r u -x r <pTTTe(v)I0(i>)exp[- e(v)cnx]

where cpT is the t r ip le t - fo rmat ion efficiency and TT the phosphorescent l i fe t ime; e(v) denotes the photoabsorption c r o s s sect ion which i s p r o p o r ­tional to the usual ext inct ions coefficient.

P o s i t r o n s en te r from an Na22 source through the opposite surface of the s lab , at x^D.5 They a r e stopped and form P s at x, with probabil i ty

- 0 at x has not yet annihilated at ty

6pPs(x) ^/3jLtexp[- \±{D -x)]6x, (2)

where /3 i s the P s yield, and ju = 49.9p c m " 1 i s the e l e c t r o n i c - m a s s absorpt ion coefficient6 in t e r m s of p , the density of the solvent in g r a m s pe r cubic cen t ime te r . In our expe r imen t s (cT

^ 10~2) the sol ids r ema in diamagnet ic under i l ­lumination with r e g a r d to P s formation in the sense that o - P s is formed re la t ive to p-~Ps in the ra t io 3:1. P r a c t i c a l l y all pos i t rons bound to an e lec t ron propagate as P s through the solid and annihilate with an e lec t ron into two y ' s : p-Vs p r e ­dominantly by self-annihi lat ion at the r a t e yp

^ (0 .2 nsec )" 1 , and o - P s by e lec t ron pickoff from the solid at the r a t e y0 ^ (1 nsec)" 1 . In compe t i ­tion with annihilation, P s encounters photomag-netic s i t e s T at the r a t e \cAx)n (x being the vol ­ume ra t e ) , where />-Ps conver t s into o - P s with probabi l i ty ap, and o - P s in to />-Ps with p robab i l ­ity a0 e i ther through P s - T compound formation or sca t t e r ing . 7 As a r e su l t , />-Ps contr ibutes to the o - P s concentrat ion in the sample at the con­vers ion r a t e Kp(x), and o - P s concentrat ion at the convers ion r a t e K0{X), where

Kp(x)=apxcT(x)n, K0(X)= a0xcT(x)n. (3)

Two coupled ra te equations govern this behav­ior , of the s ame s t r u c t u r e a s t r ea ted e a r l i e r . 8

The solution has two l ifet ime components of the probabi l i ty , 5pp5(x, t), that P s formed at the t ime

(x,t)=6pPs(x) — ^ e x p C - r y ) L 1 i 2

rt - y r\-r2

e x p ( - T2t) (4)

In the p r e sen t context y = (y p /4) + (3y 0 /4) and, s ince cT «1,

T1(x) = yp+Kp(x), T2(x) = y0 + K0(x). (5)

The exper iment r e g i s t e r s the mean two-compo­nent pos i t ron l ifet ime spec t rum of the cell a s s e m ­bly. We fold into an average shor t component the short l ived t e r m of Eq. (4) and the pos i t ron f r a c ­tion (1- /3) that annihi la tes a s " f r e e " without fo rm­ing P s with a c rO\;)-independent r a t e ~ 2 y p , and in tegra te from x = 0 to x = D. To leading t e r m s in the l ifetime r anges reso lved in our exper iment , the resu l t ing spec t rum is of the form Eq. (4) where the K'S in Eq. (5) a r e rep laced by mean convers ion r a t e s

Kp.O - ^p.O f\e9 M, D), (6)

with the abbreviat ion K?t0°= Kpo(x = 0). The func­tion

f ^[(i/{ecn ~'/z)] [ exp ( - i±D) - e x p ( - ecnD)]

accounts for the over lap between the pos i t ron -range dis t r ibut ion and the l ight - in tens i ty d i s t r i ­bution in the sample . Since £, /i, and D a r e known, the m e a s u r e d changes of Ft and T2 b e ­tween light on and light off (and the concomitant changes in the in tens i t ies of the two components) via Eq. (6) yield, r espec t ive ly , the convers ion r a t e s Kp° and K0° for the ca l ib ra ted light intensi ty I0 enter ing the cell at x = 0. The ra t io of the sp in -convers ion fac to rs is given by

/K0 = aJac (7)

The P s propagat ion r a t e follows through Eqs . (1), (3), and (6) from the m e a s u r e d dependence of *p,o° on /0.

Dilute solut ions {en ~ 10"2 m o l e / l i t e r ) of p h o s ­phorescent molecu les w e r e p r e p a r e d in the s o l ­vents cyclohexane, g lycero l , and bor ic acid. Benzene was studied p u r e . A solution was p i ­pet ted into a cell cons is t ing of thin quar tz wal ls c lamped against var iab le Teflon s p a c e r s (Z>~ 1 -2 m m ) , a Na22 pos i t ron source backed by a m e t ­al s t r i p affixed to one cel l wal l , and the a s s e m b ­ly submerged in liquid ni t rogen inside a quar tz Dewar . A h i g h - p r e s s u r e m e r c u r y l amp, with a wa te r f i l ter (to reduce sample heating) and ex -

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VOLUME 30, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 26 FEBRUARY 1973

TABLE I. Measured mean conversion rates Kp and K0 in several solid solutions. The widely ranging properties and experimental conditions are summarized in the first columns and in Table II. Our experimental data (±25% un­certain) and the inferred Ps volume-propagation rates are listed in the last four columns. Exponents of 10 are giv­en in parentheses.

Solution

C O

C.l

C.2

C.3

G.l

G.2

G.3

Solute

benzene

1,2 benzanthracene

bopq

chlorophyll

fluorescein

fluorescein

rhodamlne B

Solvent

(77°K)

—

c-hexane

c-hexane

c-hexane

glycerol

boric acidc

glycerol

en

(1019 cm"3)

6.6 ( 2)

1.8

1.2

2.4

7.2 (-1)

1.2

8.4 (-1)

cT(0)

(ppm)

5.4

1.9

7.3

1.7

2.5

1.9

3-2

(3)

(3)

(1)

(2)

(3)

(3)

(3)

*° i (p,sec-1)

158

55

144

138

103

22

103

K. P

0

1.7

2.3

1.9

2.0

1.6

1.8

1.6

(cnPsec )

1.4

2.2

7.0

9.1

5.2

1.1

3.3

(-7)

(-6)

(-6)

(-6)

(-9)

(-8)

(-8)

Abbreviation for bisbutyloctyloxy-p-quaterphenyl. bBenzene and cyclohexane are crystalline solids; glycerol and boric acid are glasses. cAt room temperature.

changable color and gray filters, illuminated the sample with accurately calibrated intensities for fixed time periods (-minutes) and was shuttered off for equal time periods. The counts of coin­cidences between the 1.3 -MeV y issuing from the Na22 source at the creation of a positron and one of the two 0.5-MeV y's emitted in the annihilation with an electron were stored separately during light on and off in the halves of a 400-channel analyzer. The two light-on and -off spectra thus accumulated concurrently during a day or so. The light-off spectra have lifetime components that are in good agreement with published data of

the solvents, and are independent of c. The life­time apparatus and the data analysis are the same as used earlier.9 Details of this experi­ment will be reported elsewhere.

Some of our results, and the conditions under which they were obtained, are summarized in Tables I and II. We have confirmed the depen­dences of the conversion rates on I0(D) and D dis­cussed above. Figure 1 shows, as an example, the linear increase of ~K0 with I0 and its variation with D, as expected from Eqs. (1), (3), and (6).

We conclude: (1) Photomagnetic Ps conversion has been observed through a dependence of posi-

TABLE II. Triplet parameters and illumination conditions of the solutions listed in Table I. Most of the T par­ameters are quoted from C. Parker, Photoluminescence of Solutions (Elsevier, New York, 1968). Exponents of 10 are given in parentheses.

Solution

C O

Col

C.2

C 3

G.l

G.2

G.3

V

(104 cm"1)

3.92

3.45

3.25

2.33

2.13

2.28

1.82

e(v)

d o " 1 6 cm2)

3.1 (-3)

1.2

1.9

2.1

6.9 (-D

9.2 (-1)

4.2

I0(v)

flO15 £ ( c r c

7.

15

62

i4o

60

520

240

hotons) sec~l)

8

9T

0.8

0.8

0.6 ?

0.24

O.85

O.85

0.3

(sec)

3.0

1.0

5 (-3) ?

4 (-3)

2.5

2.5 ?

2 ?

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V O L U M E 30, N U M B E R 9 P H Y S I C A L R E V I E W L E T T E R S 26 FEBRUARY 1973

usee

160

140

120

100

80

60

40

20

! I i l 1 1

D (mm) i

• • 5 / • Benzene /

o Rhodamine B ,

/•

- / ° / 1.7/"

/ y o

/ / / ' #

• / • o^ J>"-/ s ^^

/ S ^"^ / ' ^^ / / • ^"^ / s ^ ^ / So ^6

/ s ^"^

/^^ • 23 1 0.2 0.4 0.6 1.0

Relative Light Intensity

FIG. 1. The convers ion r a t e J^ v e r s u s light in tensi ty . The slope v a r i e s with ce l l th ickness as predic ted by Eq. (6) ( s t ra ight l ines) yielding the r a t e KO

0 independent of ce l l geome t ry . The absolute e r r o r in i^ i s ±25% ( e r r o r flag); the re la t ive e r r o r s a r e comparab le to the s c a t t e r about the theore t i ca l l i nes .

tron lifetime spectra on sample illumination. The effects can be enhanced and the accuracy of the measurements improved by altering the cell geometry and increasing the light intensity with­out inducing intolerable temperature fluctuations in the sample, e.g., through the use of lasers . (2) Within experimental e r ror , ap/a0 - 2.0 ± 0.4 is the same for all triplet states investigated here. Although a detailed discussion of this r e ­sult is outside the scope of this communication, we note that the ratio is decidedly lower than the value 3 expected for the conversion by a spin-! impurity (free radical).7 It indicates that P s - T conversion proceeds through catalysis (T remains unchanged in the process) as well as through spin flip (T converts to a singlet). (3) Since a0

is of order 1, the volume rates x vary from ~10"6 cm3 sec"1 in solid cyclohexane and ~10~7

cm3 sec"1 in solid bezene to ~10~8 cm3 sec"1 in the glycerol and boric-acid glasses. If Ps prop­agation is treated as a diffusion process,10 '11

these values indicate relatively large Ps diffusion constants for these open molecular solids, rang­ing from 10"x and 1 cm2 sec"1 in polar glasses to 10 - 1 and 1 cm2 sec"1 in the Van der Waals solids benzene and cyclohexane.

We have observed similar effects of illumina­tion on positron lifetime spectra in biological systems such as algae, but we are not sure, as yet, whether the changes indicate photomagnetic conversion proper, or whether they signify in­creases in the oxygen concentration attendant to photosynthesis.

Our gratitude goes to A. Schwarzschild for his interest and help.

*Work supported by the National Science Foundat ion. ! A. Jablonski , Nature 131, 839 (1933), and Z . P h y s .

94, 38 (1935). ""^G. N. Lewis and M. Kasha, J . A m e r . Chem. Soc. 6Q9

2100 (1944). 3G. N. Lewis and M. Calvin , J . A m e r . Chem. Soc. 67,

1232 (1945); G. N. Lewis , M. Calvin, and M. Kasha , J c Chem. P h y s . 17_, 894 (1949).

4 For a r ecen t rev iew, cf. J . B . B i r k s , Photophysics of Aromatic Molecules (Wi ley- In te rsc ience , New York, 1970).

E x p e r i m e n t s with pos i t rons enter ing with the light at x = 0 show that our r e s u l t s a r e independent of g e o m e ­t ry .

6 L. Katz and A. S. Penfold, Rev. Mod. P h y s . 24, 28 (1952).

7 F o r a detai led d i scuss ion of P s convers ion by s table pa ramagne t ic i m p u r i t i e s , cf. J . D. McGervey, in Posi­tron Annihilation, Proceedings of the International Con­ference 1965, edited by A. T. Stewart and L. O. Roe l -lig (Academic New York, 1967), p . 143 ff.

8W. Brandt , in Positron Annihilation, Proceedings of the International Conference 1965, edited by A. T. S te ­war t and L. O. Roellig (Academic, New York, 1967), p . 178.

9W. Brandt , H. F . Waung, and P . W. Levy, P h y s . Rev. Lett . 26, 496 (1971).

10W. Brandt and H. F . Waung, P h y s . Rev. B 3, 3432 (1971).

U W. Brandt and R. Paul in , P h y s . Rev. B £ , 2430 (1972).

357