The angular and spectral distribution of transition radiation from thin silver foils

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The angular and spectral distribution of transition radiation from thin silver foils

E.T. Arakawa, N.O. Davis, L.C. Emerson, R.D. Birkhoff

To cite this version:

E.T. Arakawa, N.O. Davis, L.C. Emerson, R.D. Birkhoff. The angular and spectral distribution of transition radiation from thin silver foils. Journal de Physique, 1964, 25 (1-2), pp.129-133.

�10.1051/jphys:01964002501-2012901�. �jpa-00205722�

129

REFERENCES [1] ^MADDEN (R. P.) and CANFIELD (L. R.), ^J. Opt. ^Soc.

Am., 1961, 51, ^838.

[2] ^HUNTER (W. R.), Proc. Xth Colloquium Spectrosco- picum Internationale, Spartan ^Books, Washington,

D. C., 1963, p. 247.

[3] ^TOUSEY (R.), ^J. Opt. ^Soc. Am., 1939, 29, 235.

[4] ^SIMON (I.), ^J. Opt. ^Soc. Am., 1951, 41, 336.

[5] ^MADDEN (R. P.), ^CANFIELD (L. R.) ^{and HASS} (G.),

J. Opt. ^Soc. Am., 1953, 53, 620.

[6] ^ROBIN (S.), C. R. Acad. Sc.,1953, 236, 674.

[7] ^SCHULZ (L. G.), ^J. Opt. ^Soc. Am., 1954, 44, ^357.

[8]

SCHULZ (L.

G.) and TANGHERLINI (F. R.), ^J. Opt. ^Soc.

Am., 1954, 44, ^362.

[9] ^COLE (T. ^{T.) and} OPPENHEIMER (F.), Applied Optics, 1962,1, ^709.

[9a] ^WALKER (W. C.), ^RUSTGI (O. P.) ^{and WEISSLER} (G. L.), ^J. Opt. ^Soc. Am., 1959, 49, 471.

[10] ^FROHLICH (H.) ^{and PELZER} (H.), ^Proc. Phys. Soc., 1955, ^A 68, ^525.

[11] ^ROBINS (J. L.), ^Proc. Phys. Soc., ^1961, 78, ^1177.

[12] ^JACOBUS (G. F.), ^MADDEN (R. P.) ^{and CANFIELD} (L. R.), ^J. Opt. ^Soc. Am., 1963, 53, ^1084.

THE ANGULAR AND SPECTRAL DISTRIBUTION OF TRANSITION RADIATION FROM THIN SILVER FOILS

By

^E.

T. ARAKAWA,

^{N. O.}

DAVIS,

^{L. C.} EMERSON and R. D.

BIRKHOFF,

Health Physics Division, ^Oak Ridge ^National Laboratory (1), ^Oak Ridge, ^Tennessee.

Résumé. ²⁰¹⁴ On a déterminé expérimentalement les distributions angulaire ^et spectrale, ^{dans le}

domaine de longueurs d’onde de 2 500 Å à 5 600 Å, ^de _photons émis par ^des feuilles d’argent ^de

660 Å et 1 980 A d’épaisseur lorsqu’on les bombarde avec des électrons de 40 keV. La distribution

spectrale de la lumière polarisée ^{dans le} plan d’incidence a montré un maximum aigu ^à

3 300 Å ± ¹² Å. Cette valeur est une moyenne évaluée ^sur 1’ensemble des directions faisant avec

la normale à la feuille des angles ^allant de 10° à 50°. En plus ^{de ce maximum, le} spectre présentait

un fond continu dont l’intensité décroissait lentement lorsque ^la longueur ^d’onde augmentait,et

un faible minimum à 3 200 A, suivi, pour les longueurs ^d’onde plus ^{courtes, d’une} augmentation

d’intensité. La distribution angulaire ^des photons émis, pour la longueur ^d’onde correspondant

au maximum, présente ^{un maximum à 30°} de la normale à la feuille. Aucun photon ^{n’est émis} perpendiculairement ^ou tangentiellement ^à la feuille. En revanche, la lumière émise pour d’autres

longueurs d’onde du fond continu, par exemple ^{2 700 Å et 4 500} A, était surtout intense à 50°

de la normale. On a déterminé le rendement lumineux absolu après avoir étalonné le spectro- mètre, l’analyseur ^{et Ie} photomultiplicateur ^{avec une} lampe ^à filament de tungstène provenant

du U. S. National Bureau of Standards. En ce qui ^concerne les directions faisant un angle ^{de 10°.}

à 40° avec la normale, le rendement lumineux était en tout point ^{en accord avec les} prévisions théoriques pour toutes les longueurs ^d’onde sauf pour celle correspondant ^{au maximum} aigu

pour laquelle la valeur expérimentale ^est inférieure de 30 % ^environ.

Abstract. ²⁰¹⁴ The angular ^and spectral distributions of photons ^emitted

by Ag

^{foils 660 Å and}

1 980 Å in thickness when bombarded by ⁴⁰ keV electrons have been determined experimentally

in the wavelength region ^{from 2 500 A to 5 600 Å. The} spectral distribution of light polarized

in the plane ^of incidence showed a sharp peak ^{at 3 300 Å ± 12} Å, ^this value being ^an average

over photon directions from 10° to 50° from the foil normal. In addition to the peak, ^the spectrum

showed a continuum which decreased slowly ^with increasing wavelength ^{and a} deep ^minimum

at 3 200 Å with a rise in the shorter wavelengths. ^The angular distribution of photons ^emitted

at the peak wavelength ^{showed a maximum at 30° from the} foil normal with zero intensity ^{at 0°}

and near 90°, whereas the photons emitted at other wavelengths ^{in the} continuum, e.g., 2 700 A

and 4 500 Å, ^{were most} intense at 50° from the foil normal. The absolute photon yield ^{was deter-}

mined by calibrating ^the spectrometer, analyzer, ^and photomultiplier ^{with a} tungsten ^filament lamp obtained from the U. S. National Bureau of Standards. For photon directions from 10°

to 40° the photon yield ^{was found} to agree with the theoretical predictions ^{in all} respects ^{at all} wavelengths except at that of the sharp peak ^{where the} experimental ^{values were about 30} %

lower.

JOURNAL DE PHYSIQUE TOME 25, JANVIER-FÉVRIER 1964,

Introduction. ^- In 1945 Frank and

Ginsburg [1]

predicted

that radiation would be emitted when ^a

uniformly moving

^electron

passed

^{from one}

medium into another. To

explain

^the

pheno-

(1j Operated by Union Carbide Corporation ^{for the}

U. S. Atomic Energy Commission.

menon of this " transition radiation

", they

^consi-

dered an electron

passing

^{from a vaccum into a}

perfect

conductor. While

approaching

^{the con-}

ductor the

electromagnetic

^{field in the vacuum is}

equal

^{to the field of the} electron and of its

image moving

towards it. From the

point

^{of view of}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002501-2012901

the field in the vacuum the electron and its

image

cease to exist ^once the electron crosses the boun-

dary

^{between them. The} radiation emitted would be the same as that

resulting

from the sudden annihilation of the electron and its

image

^{at the}

interface.

Ferrell

[2]

^has

recently

^{shown that}

plasma

^oscil-

lations within a thin metal film can

occasionally decay by photon

^emission.

Thus,

whenever the electron

plasma

^{of a} metal film is excited

by

^the

passage of ^a

charged particle,

^{radiation will be}

emitted at a

frequency

characteristic of the

plas-

mon energy. The

angular

distribution of the

plasma

^{radiation follows a} modified cosine law.

A

generalization

of the transition radiation

theory

^was

presented by

Ritchie and

Eldridge [3].

They

showed that

photon

^{emission can be}

expected

from a solid not

only

^{at the}

plasmon

energy ^where the collective excitations in solids _occur, but also around the interband transition energy where

single particle

excitation occurs. Ritchie’s expres- sion reduces to Ferrell’s result in the non-relati- vistic limit when the dielectric constant is taken to be that of a free electron _gas.

Silver,

which has been the element most tho-

roughly investigated,

^{emits a}

sharp peak

^{at 3 300 A}

in addition to a continuum at

longer wavelengths.

The relative

intensity

^{of this}

peak

^for

angles

between 100 and 800 from the normal on the

emergent beam side has been

reported by Brown, Wessel,

and Trounson

[4]

for foils of 500 A thick-

ness.

Frank,

Arakawa, and Birkhoff

[5] reported .

the

complete

spectrum ^{from 800} A foils at

angles

of

2°, 4°, 300,

and 720. Their results showed

good

agreement with theoretical

predictions.

^{A sum-}

mary of other

experiments

^on transition radiation is

given

in this paper.

Experiment.

^{- The} apparatus ^{used in}

this investigation

^{is shown in}

figure

^{1. The}

spectral

distribution of

photons

^emitted

by Ag

^{foils 660 A}

and 1980 A thick bombarded

by

40 keV electrons

was determined in the

wavelength region

^from

2 500 A ^{to 5 600} A. The

experiment

^{was carried}

out for

angles

^{between 00 to 1500 with} respect ^to

the foil normal

using

^an

angular

distribution chamber which

permitted

^the spectrometer ^{to be}

rotated around the foil in a continuous fashion without

breaking

^{the vacuum. A}

Glan prism

^ana-

lyzer

^{was used to} separate ^the

light

into compo- nents

polarized parallel

^and

perpendicular

^{to the}

plane

of the electron and

photon.

Transition radia- tion was shown

by

Frank and

Ginsburg

^{to be}

polarized

^{in the}

parallel plane,

whereas brems-

strahlung

^has components ^{with both}

polarizations.

The

experimental

^{results for the}

parallel pola-

rized radiation were

compared

^{with the}

predictions

of the Ritchie and

Eldridge theory

^{on an absolute}

basis for emission from both the front and back surfaces of the silver foils. The

optical

^constants

required

^{for the} theoretical

interpretation

^were

obtained from the results of Ehrenreich and

Philipp [6].

^These

comparisons

^for

angles

^less

than 900 are shown in

figures

2 and 3 for 660 Å

silver foils with electron

energies

of 40 keV. For the small

angles (6

^{= 50 to}

40°),

the observed

peak

at À ⁼ 3 300

A

is less intense than that

predicted by theory.

The continua on both sides of the

FIG. 1. ^- Schematic diagram ^of accelerator, angular distribution chamber, ^and spectrometer.

FIG. 2. ^- Theoretical and experimental spectra ^from Ag ^{foil 660 A thick.}

FIG. 3. ^- Theoretical and experimental spectra ^from Ag ^{foil 660 A thick.}

peak

agree

closely

^with

theory.

^The

spectral

^dis-

tributions at the

larger angles (6

^{= 500 to}

870)

show

good

agreement ^{with the}

theory

^{for all wave-}

lengths.

The

experimental spectral

distributions for the

same foil at

angles larger

^{than 900 are}

compared

with

theory

ⁱⁿ

figures

^{4 and 5.}

Very

close agree- ment at these

angles

^{was found}

throughout

^the

entire

wavelength region

^studied.

Also,

^{in the}

same

figures

^the

spectral

distributions of the radia- tion emitted from the back surface are

compared

with those from the front surface at

corresponding angles.

^The

intensity

from the front surface is

higher

because of relativistic effects.

The

intensity

^{at the silver}

peak

^{as a} function of

angle

for the 660 A foil is shown in

figure

^{6. The}

FIG. 4. ^- Theoretical and experimental spectra ^for corresponding angles ^{on front}

and back sides of Ag ^{foil 660} A thick. (6 ^{= 500 vs} 130°.)

FIG. 5. ^- Theoretical and experimental spectra ^for corresponding angles ^{on front}

and back sides of Ag ^{foil 660} A thick. (0 ⁼ 60°, 700, ^vs 1200, 110°, ^{and E = 40} keV.) solid line

represents

^the

theory

^while

points

^labeled

with + and ^o represent ^the

experimental

^data

obtained with two foils of the same thickness. The measured

angular

distribution shows a maximum

intensity

^{at 300 in} agreement ^with

theory,

^{but the}

observed

intensity

^{is not as}

large

^as

predicted

^for

the smaller

angles (0

^{400 and 0} >

140°).

^A

comparison

^between

experiment

^and

theory

^at

X ⁼ 4 500 A and 2 700 A in the same

figure

^shows

good agreement

for both the

angular

distribution and

intensity.

The maximum intensities for the continua occur at 0 ⁼

50°,

whereas the maximum

intensity

^{for the 3 300}

^A peak

^{occurs at 300.}

The

experimental

results for the

light

^{emitted in}

FiG. 6. ^- Comparison ^between theory ^and experiment ^of

the angular distribution at X ⁼ 2 700 A, ^{3 300} A, ^and

4

500 A

^for Ag ^{foil 660 A thick.}

the

perpendicular plane

^for

angles

^{less than} 90°

by

a foil 1 980

A

thick are shown in

figure

^7.

Although

^detailed conclusions

concerning

^this

source of radiation cannot be

presented

qecause the observed

intensity

^was

only

^{two to three times}

the noise

level,

^some

general

trends may be seen.

The

intensity

is maximum in the direction of the electron beam and decreases with

increasing angle

as is

predicted by bremsstrahlung theory.

^The

photon intensity

^{for the 1980 A foil is} greater

than for the 660 A foil as

expected

for brems-

strahlung.

The results of this

investigation

^{show that a}

complete description

of the transition radiation emitted

by

electron-bombarded thin silver foils may be obtained from the

theory

^of Ritchie and

Eldridge using

the dielectric constants of the metal determined in a separate

optical experiment.

^The

spectral

distribution of the transition radiation

intensity

^{as a function of}

angle

from the foil

normal,

^{the absolute}

photon intensity,

^{and the}

FIG. 7. ^- Experimental results for the light emitted in the

perpendicular plane ^{on the} front side of ^a Ag ^{foil 1 980 A}

thick (E ^{= 40} keV).

polarization

^{were studied}

experimentally

^and

found to show

good

agreement ^with

theory.

The

intensity

^of

photons

^{emitted in} the perpen- dicular

plane

^{which was ascribed to}

bremsstrahlung

was not as well determined because of the low

intensity. However,

^{the results} suggest that inves-

tigation

^of

bremsstrahlung

^{in the}

optical region

^is

feasible

using

^the

techniques

described.

Discussion

M. MAYER. - How does the

intensity

^{of the}

transition radiation

depend

^on the energy of the incident electrons ?

Reponse :

^The

intensity

^increases

linearly

^with

electron energy.

Reponse

^{de M. ARAKAWA a une}

question

^de

M. TRICOLES :

The index of refraction varies from less than one

to about 1.4 in this

wavelength region.

REFERENCES [1] ^FRANK (I. M.) and GINSBURG (V. L.), ^J. Phys., USSR,

1945, 9, 353.

[2] FERRELL (R. A.), Phys. Rev., 1958, 111, ^1214.

[3] ^RITCHIE (R. H.) ^{and ELDRIDGE} (H. B.), Phys. Rev., 1962,126,1935.

[4] ^BROWN (R. W.), ^WESSEL (P.) ^{and TROUNSON} (E. P.), Phys. ^Rev. Letters, 1960, 5, ^472.

[5] ^FRANK (A. L.), ^ARAKAWA (E. T.) ^{and BIRKHOFF} (R. D.), Phys. Rev., 1962, 126, ^1947.

[6] EHRENREICH (H.) and PHILIPP (H. R.), Phys. ^Rev., 1962, 128, 1622.