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HAL Id: jpa-00215777

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ON THE COMPENSATION OF A NONUNLFORM CHEMICAL (MONOPOLE) SHIFT OF THE

MÖSSBAUER LINE

V. Gol’Danskii, S. Karyagin, V. Namiot

To cite this version:

V. Gol’Danskii, S. Karyagin, V. Namiot. ON THE COMPENSATION OF A NONUNLFORM CHEMICAL (MONOPOLE) SHIFT OF THE MÖSSBAUER LINE. Journal de Physique Colloques, 1974, 35 (C6), pp.C6-193-C6-196. �10.1051/jphyscol:1974620�. �jpa-00215777�

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JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 12, Tome 35, Dtcembre 1974, page C6-193

ON THE COMPENSATION

OF A NONUNIFORM CHEMICAL (MONOPOLE) SHIFT OF THE MOSSBAUER LINE

V. I. GOL'DANSKII, S. V. KARYAGIN

Institute of Chemical Physics, Academy of Sciences of the USSR, 117334, Moscow and V. A. NAMIOT

Nuclear Physics Research Institute

Physics Department of the Moscow State University 117234, Moscow

Resume. - La proportionnalite entre la densite totale d'electrons S et la densite de spin au site du noyau permet de proposer une methode pour compenser par un champ de radio-frequence approprie la raison essentielle d'elargissement des raies Mossbauer : le deplacement isomerique non uniforme.

La methode proposke pour restreindre la largeur des raies Mossbauer peut &re appliquk a la deter- mination precise de certains paramttres d'i. h. f. et I'elaboration d'un laser y (gaser). Elle est egale- ment importante pour l'extension de la spectroscopie Mossbauer ?tous les problhmes nkcessitant i des raies plus Btroites (probablement jusqu'a la largeur de raie minimale de RMN en phase solide, c.-a-d. 10-15 eV).

Abstract. - The proportionality between the small variations of total S-electron density and spin density at the site of nucleus location permits proposing a method of compensating by a pro- perly chosen radiofrequency field the most essential source of Mossbauer line broadening : the non-uniform chemical (monopole) shift. The proposed method for narrowing of the Mossbauer lines can be used for precise determination of certain HFS parameters and for starting the operation of a y-laser (gaser). It is also important for the extension of Mossbauer spectroscopy to all problems, which need much narrower lines (probably, up to the minimum width of solid state NMR line, i. e. ca 10-15 eV).

In real crystals the chemical (monopole) shift (I) of (HFS) nuclear levels, proportional to the total density of electrons on this nucleus [I], varies from nucleus to nucleus. For long-lived isomers this results in broadening of the Mossbauer line that exceeds then 'the natural line width by many orders of magnitude [2].

This is the most essential impediment to use of long- lived isomers in gamma-resonance (Mossbauer) spec- troscopy and for producing of y-lasers (gasers) [2, 3,4], since it seemed that such a broadening cannot be suppressed by radio-frequency methods [4, 51, the monopole shift being the same for all HFS com- ponents.

A method is proposed for compensating the varia- tion in the monopole shift of a Mossbauer line by that of H F splitting of an opposite direction and the same value. The H F splitting variation may be for instance due to a change in the Fermi contact interaction that is proportional to the electron spin density on the nucleus [6]. Such a compensation is possible in a pro- perly chosen periodical homogeneous magnetic field.

The choice of a crystal compound for which small variations in the total electron density on the nucleus

(1) The chemical shift in Mossbauer spectra is called the isomer or monopole shift to distinguish it from the chemical

shift in NMR, which has somewhat different nature.

are proportional to these in the spin density is assumed to be possible.

The alternating magnetic field is applied in order to attain a compensating value for the coefficient of pro- portionality between variations in the monopole shift and H F splitting.

It will be noted that HFS in the alternating field is determined for the quasi-energy of the nucleus [7, 81.

The most simple theoretical case would be that, when the spin of the ground state is zero, and the static homogeneous magnetic field H circumscribes a cone with top angle 2 8 around axis Z with a frequency o.

Making use of the Majorana theorem [9] and of the solution for a Majorana pseudo-particle [9, 101 with spin

5,

the HFS for the nucleus quasi-energy A with spin I, magnetic moment p, and monopole shift ti6 will be

where m = - I,

-

I

+

1,

..

., I are the eigenvalues of spin projection onto the direction of the rotating field, o, = pHl(2 Ifi) is the Larmor precession frequency of the Mayorana pseudo-particle in field H.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974620

(3)

C6-194 V. I. GOL'DANSKII, S. V. KARYAGIN

Field H is the sum of the external field He and the effective field Hf due to Fermi interaction, i. e.

H = He

+

Hf. (3)

when

where p, is the electron magnetic moment, T is the temperature, K is the Boltzmann factor. When (4) is fulfilled, the effective field Hf continuously follows the direction of He without essential fluctuations [lo].

It will be taken into account that

S = < 8 > + A S ; H f = < H f > + A H f (5) where parentheses

<

A

>

stand for a certain value A averaged over all nuclei, and AA defines the deviation of A from

<

A

>.

It follows from the assumption of proportio- nality between small variations in electron and spin densities (2) on passing from nucleus to nucleus that

A AS = KP AH, (6)

where K is a dimensionless constant that can be of the order 0.01-0.1 [11, 12, 131.

Dropping the small values of order

I

A H f / H 1' in (2) we obtain

where the value C, standing for the compensation coefficient of the mth HFS component is

With proper' selection of values ,w, 9; He the mth component of the quasi-energy HFS can become zero.

This would require fulfilment of the co'mpensation condition

C m = L I C . (9)

When o = - 2

<

ww

>,

eq. (9) reduces to

Then the condition for compensation of monopole broadening will be

He > T x 1 0 4 0 e / g r a d ; IC 4 I"; w = - 2

<

OM

>

;

(2) Note, that we are dealing here with the proportionality between small variations of isomer shift 6 and local magne- tic field at the nucleus Hf (e. g. due to the change of the volume of elementary cell caused. by various imperfections of the crys- tal - see [Z]) rather than with the (non-existent) proportionality between above-mentioned magnitudes themselves

(8 a 1 ~ ( 0 ) 1;

+

~ v ( O ) I ~ and H f 1 d o ) 1: - If) .

H , is the amplitude of the alternating (rotating) part of the field (3). For instance, at T = 0.1 K ; K = 0.01 ; I = 2 ; 1 m I = I ; pH = 3 x eV, we must have w/2 The compensation method could be used as a cer- n

-

40 MHz, He > lo3 Oe, Hi > 20 Oe.

tain spectroscopic means ibr determination of HFS characteristics such as IC = h A6/p AHf and p(He

+

Hf).

Indeed, let product rn sin 9,/2 be the same for all compensating angles 9, at a constant frequency w.

Then [ K / and p(H,

+

Hf) can be readily obtained from (lo), as the latter will be valid only provided o = - 2 < o , > .

As to application of the method to gasers, fast applying of the compensating radio-frequency field, with other critical conditions fulfilled, is equivalent to the opening action of a shutter in common lasers.

The method can be used for a more common form as well. Then the field H = He

+

Hf = (He

+

H f ) n will change both in direction n, as in the above case, and in the value of He

+

H f . Using the method of Hamiltonian reduction over the s-matrix, in the same way as this was done by one of the authors 151, the field H and the compensation coefficient can be expressed in a parametric form

A I

H , = -

[j

cos $

+

( 6

+

2 A) sin y sin

$1

;

P

(11) ' I [ - ;sin$

+

( 6

+

21)sin y cosd];

H,, =

-

Ir

The compensation condition retains its form (9).

Here o / 2 n is the fundamental frequency of the compensating radio-frequency signal ;

where p, g, r are arbitrary integers ; &t), &(t), {(t) are arbitrary periodical functions of period T ; A is an arbi- trary real constant over the range

(3) Note the difference in' signs of w and < o~ >. The field must rotate in a direction opposite to nuclear precession.

(4)

ON THE COMPENSATION OF A NONUNIFORM CHEMICAL (MONOPOLE) SHIFT C6-195

6,

I), are the first time derivatives :

In principle, the three arbitrary functions and on free constant il make possible not only the fulfilment of the condition for compensation of monopole broa- dening (9), but also suppression by radio-frequency methods 14, 51 of the magnetic and electric quadrupole variations in the monoljole shift.

The idea of compensation by means of a controlled radio-frequency field can be extended to a more complex case, when both isomer states have non-zero spins, and the HFS represents a superposition of the monopole shift and of the magnetic and quadrupole H F interactions (HFI).

As in the model case, this would require a crystalline compound for which variations in local HFI on passing from nucleus to nucleus would be proportional to those in the monopole shift. Then, similarly to the above, proper selection of the radio-frequency field would make possible a situation such that the fluctua- tions of the total magnetic-quadrupole HFI and those of the monopole shift for one of the HFS components would appear to be mutually compensated (4). More- over other HFS variations not proportional to those of the monopole shift can also be compensated by using a more complex compensating fields.

(4) Not only the constant variations can be compensated, but also the fluctuations in the monopole shift slowly changing with time (in terms of the radio-frequency signal period).

References

[I] BODMER, A. R., Nucl. Phys. 21 (1961) 347.

[2] GOLDANSKII, V. I., KAGAN, Yu. M., Usp. Fiz. Nauk 110 (1973) 445.

[3] RIVLIN, L. A., RUSS. Pat. No 709414126 of January 10, 1961 and No 710508 of April 1,1961.

[4] IL'INSKII, Yii. A., KHOKHLOV, R. V., Usp. Fiz. Nauk 110 (1973) 449.

[5] NAMIOT, V. A., Letters to ZhETF18 (1973) 369.

[6] FERMI, E., Z S . Phys. 60 (1930) 320.

[7] NIKISHOV, A. I.. RITUS, V. I., Zh. Eksp. Teor. Fiz. 46 (1964) 776.

[8] ZEL'DOVICH, Ya. B., Usp. Fiz. Nauk 110 (1973) 139.

[9] LANDAU, L. D., LIFSHITS, E. M., Kvantovaya Mekhanika Fizmatgiz, 1963.

[lo] GOL'DMAN, I. I., KRIVCHENKOV, V. D., Sbornik Zadach po Kvantovoi Mekhanike, GIITL, Moscow, 1957, No 19 sect. 6.

[11] AL'TSHULER, S. A,, KOZYREV, B. M., Elektronnyi Para- magnitniyi Rezonans, Fizmatgiz, Moscow, 1961.

[12] GOLDANSKII, V. I., Effekt Mossbauera i ego Primenenie v Khimii, Akad. Nauk USSR, Moscow, 1963.

1131 KISTNER, 0 . C., SUNYAR, A. W., Phys. Rev. Lett. 4 (1960) 412.

The modern literature on gasers (gamma-lasers) and directly related problems

a ) PUBLICATIONS IN URSS.

1. GOLDANSKII, V. I. and KAGAN, Yu., (< On the Possibility of Creating a Nuclear Gamma-Laser >).

a ) Preprint of the Institute of Chemical Physics of the Aca- demy of Sciences of the URSS. (Reported on June, 7, 1971) March, 15, 1972 (in Russian and in English) 22 pages.

b) ZhETF 64 (1972) 90-97, in Russian ; Sov. Phys. JETP, in English.

2. KHOKHLOV, R. V., <<TO the Possibility of Creation of y- Lasers on the Base of Radioactive Crystals )). ZhETF Pis'ma 15 no 9 (1972) 580-583, in Russian ; Sov. Phys.

JETP ,Letters, in English.

3. ARUTYUNYAN, E. A., ((Induced Mossbauer Radiation H.

Preprint of the Institute of Physical Investigations of the Academy of Sciences of the Armenian SSR, no 72-08 (1972).

4. GOLDANSKII, V. I. and KAGAN, Yu., (<On the Principle Possibility of the Creation of y-Laser (Gaser) on Nuclear Transitions P. Uspekhi Fiz. Nauk 110 (1973) 445-448, in Russian ; Sov. Phys. Uspekhi 16 (1974), in English.

5. IL'INSKII, Yu. A. and KHOKHLOV, R. V., (( On the Possibility of Observation of Stimulated y-Radiation )). Uspekhi Fiz. Nauk 110 (1973) 449-451, in Russian ; Sov. Phys.

Uspekhi 16 (1974), in English.

6. LETOKHOV, V. S., (( On the Uses of Lasers in Nuclear Spec- troscopy )). Uspekhi Fiz. Nauk 110 (1973) 451-452, in Russian ; Sov. Phys. Uspekhi 16 (1974), in English.

7. LETOKHOV, V. S., ((TO the Problem of y-Laser on Nuclear Transitions)). ZhETF 64 no 5 (1973) 1555-1567, in Russian ; Sov. Phys. JETP, in English.

8. GOLDANSKII, V. I., KAGAN, Yu., NAMIOT, V. A., <<TWO- Stage Excitation of Nuclei to Obtain Stimulated Gamma-Quantum Emission )>. ZhETF Pis'ma 18 no 1 (1973) 61-63, in Russian ; Sov. Phys. JETP Letters, in English.

9. IL'INSKII, Yu. A. and KHOKHLOV, R. V., Narrowing of the y-Resonance Line in the Crystals by means of RF- Fields )). ZhETF 65 no 4 (1973) (lo), 1619-1625, in Russian ; Sov. Phys. JETP, in English.

10. NAMIOT, V. A., (( Forced Narrowing of Line and the Moss- bauer Effect for Long-lived Isomers >>. ZhETFPis'ma 12 no 6 (1973) 369-373, in Russian; Sov. Phys. JETP Letters, in English.

11. KOKORIN, V. V., Los', V. F., On the Induced Generation of y-Rays in Crystals )). Fizika Tvyordogo Tela 15 no 6 (1973) 1776-1780, in Russian ; Sov. Phys. Solid State, in English.

12. LETOKHOV, V. S., (( Pumping of the Nuclear Levels by X- Radiation of Laser Plasma D, Collection of Papers

(< Kvantovaya Elektronika )) (Quantum Electronics) no 4

(16) (1973) 125-127, in Russian.

13. GOLDANSKII, V. I. and KAGAN, Yu., ((On the General Principles and Problems of Realization of Gasers (Gamma-Lasers) )). Proceedings of the Fifth Inter- national Conference on Mossbauer Spectrometry (Bra- tislava, September 1973).

(5)

C6-196 V. I. GOL'DANSKII, S. V. KARYAGIN 14. GOLDANSKII, V. I., KARYAGIN, S. V., NAMIOT, V. A., On b) PUBLICATIONS IN USA.

the Compensation of Inhomogeneous Chemical (Mono- i ole) shift of ~ o s s b a u e r ~ i n e )> (short variant this

1. BALDWIN, G. c., (< rS there a High Frequency Limit to Laser publication in Proceedings of Bendor Conference). Action ? >> (Presented at the 3rd RPI Workshop ZhETF Pis'ma 19 no 10 (1974) 625-627, in Russian; Conference on Laser-Plasma Interactions, Troy, New

JETP Letters, in English. York, on August, 14,1973).

15. VORONTSOV, V. I. and VYSOTSKII, V. I., (( TO the Question of

~ iof stimulated ?-liadiation in the ~~ ~ ~ i ~ ~ ~~ 2. DOUGLAS, ~ ~ iJ. H. (an Interview with G. C.BALDWIN), t i ~ ~ (( Russian Regime >>. ZhETF66 no 5 (1974) 1528-1536, in Russian ; Progress on the Nuclear Laser >) (Science News) 105, no 1

Sov. Phvs. JETP. in English.

-

(1974) 8-9.

KAGAN, Yu., ((On the Suppression of the Broadening of Mossbauer Line Caused by the Inhomogeneous Isomer Shift >>. ZhETF Pis'ma 19 no 12 (1974) 722-725, in Russian ; Sov. Phys. JETP Letters, In English.

KAGAN, Yu., ((The Use of the Effect of Anomalous Trans- mission for Getting the Stimulated Emission of p- Quanta in Crystals >). ZhETF Pis'ma 20 no 1 (1974) 27- 30, in Russian ; Sov. Phys. JETP Letters, in English.

18. IL'INSKII, Yu. A. and NAMIOT, V. A., (( On the Amplification in Gamma-Laser >>. Kvantovaya Radiofizika (Quantum Radiophysics) no 7 ( 1 974) 1608.

19. NAMIOT, V. A., (( TO the Question of the Broadening of Line and the Induced Radiation in Gamma-Lasers Based on Mossbauer Transitions )>. Fizika Tvyordogo Tela (in print), in Russian ; Sov. Phys. Solid State, in English.

20. DMITRIEV, V. F. and SHURYAK, E. V., On the possibilities of Creation cr a y-Laser )>, ZhETF 67 no 2 (8) (1974) 494- 502, in Russian.

3. BALDWIN, G. C., ((New Look at the Graser a ; (( Laser Focus B, March 1974.

4. BALDWIN, G. C., (< Research Problems in the Development of Gamma-Ray Lasers )) (Presented to the Optical Society of America, 1974 Annual Spring Meeting, Symposium on Ultraviolet and X-ray Lasers, April 25,1974), see the abstract in Bull. Amer. Opt. Society, paper ThA4.

5. WOOD, L., CHAPLINE, G., SLUTZ, S., NUCKOLLS, J., (( X-Ray and pRay Laser Studies at the Lawrence Livermore Laboratory )) (Presented to the Optical Society of America, 1974 Annual Spring Meeting, Symposium on Ultraviolet and X-Ray Lasers, April 25, 1974), see the abstract in BUN. Amer. Opt. Society, paper ThA3 and the full text as a preprint UCRL-75382 (1974), see also the preprints UCRL-75184 (1973) and UCRL-75255 (1973) of the Radiation Laboratory of the University of California.

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