Penetration and Diffusion of X Rays

Fano, U.; Spencer, L. V.; Berger, M. J.

doi:10.1007/978-3-642-45920-7_2

Cited by 85 publications

(38 citation statements)

References 45 publications

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“…We can follow reference [6] farther by defining an "error build-up" function Eb (z), 2 See Appendix B for a discussion of the automatic exclusion of functions having all moments zero.…”

Section: Bounds To Truncation Errorsmentioning

confidence: 99%

“…was derived from the differential equation, using eq (17.16'), both given on p. 744 of reference [2]. The recursion approach eventually breaks down, particularly for large values of k; hut with suitable restrictions, and depending somewhat on the size of the argument z, 30-40 terms gives accurate results.…”

Section: Appendix a A Plural-series Computer Programmentioning

confidence: 99%

“…In the moment me thod of calculating space distributions in radiation trans port theory, spatial moments defined by n. -x (I') are evaluated by numerical integration of a re cursive system of Volterra integral equations of the second kind [1 , 2),1 For any of several re asons , one frequently encounters the problem of constructing distributions by use of alternate, rather than consecutive moments [2,5] . Because spatial trends, are basically exponential, this leads to the possibility of representations in a family of biorthonormal systems of polynomials U~(z) , with adjoint polynomials U~(z) , satisfying the condition rX dzz"e-Z{;A·(z)Uk (z) = 011111 ,…”

Section: Introductionmentioning

confidence: 99%

“…Existence of these problems led very early to use of nonlinear approximations which were designated "function-fitting" methods , in which the individual terms in an approximating series have the same functional form, with differing weight and differing scale factor [2]. While very useful, and in good agreement with the more basic polynomial representation, these methods have the limitation that it is difficult to assess their accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Plural-series approximations of functions

Spencer¹

1972

J. RES. NATL. BUR. STAN. SECT. B. MATH. SCI.

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A me thod is give n for de veloping a pproximati ons to neutron and gamma-ray transport di stributions in the form of a superposition of U~ polyn omial series multiplied by expone ntials and charac te rized by differe nt scale fa ctors. Converge nce co ndition s a nd e rror bound expressions are give n. Biorthogonality properties are worked o ut. Examples are give n in which th ese approximati ons are compared with polyn omial approxim a tions .Key words: Biorthogo n al fun ction; gamma-ray tra ns port ; mom e nt me thods ; ne utron tran s port ; polynomial re prese ntations; radiation pe net ration.

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“…We can follow reference [6] farther by defining an "error build-up" function Eb (z), 2 See Appendix B for a discussion of the automatic exclusion of functions having all moments zero.…”

Section: Bounds To Truncation Errorsmentioning

confidence: 99%

Section: Appendix a A Plural-series Computer Programmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Plural-series approximations of functions

Spencer¹

1972

J. RES. NATL. BUR. STAN. SECT. B. MATH. SCI.

Self Cite

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“…There is an important class of radiation transport problems for which it is feasible to calculate spatial moments (I') by numerical integration of a recursive system of Volterra integral equations of the second kind [1,2].1 A detailed description of the proce,'ure for obtaining and evaluating these equations is not pertinent to the discussion here; but it is important that accurate calculation is feasible only for a limited number of the moments, say 6 to 10.…”

Section: Introductionmentioning

confidence: 99%

Bounds to truncation errors in biorthogonal polynomial approximations, with illustrative applications to gamma ray transport distributions

Spencer¹

1971

J. RES. NATL. BUR. STAN. SECT. B. MATH. SCI.

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Problems of gamma ray and ne utron penetration in infinite, homogeneo us media ca n be so lve d in ter ms of infinite s um s of a ce rtain type of biorthogonal po lyn"mial sys tem . Many ca lcu lation s have used a few te rm s, pe rhap s 4 to 8, successfu lly due to good apparent converge nce. This paper develops express ion s for bounds to th e truncati"n error of thes e finite sums. Examples and aplJlieations are given of th e functions u sed to obtain the error bounds.

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X‐Ray Quantum Cutting Scintillator Based on CsPbCl_xBr₃₋_x:Yb³⁺ Single Crystals

Song

Wang

et al. 2023

Laser & Photonics Reviews

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Metal-halide perovskites, especially for 3D halide perovskite single crystals (SCs), are emerging as the promising scintillators. However, the strong self-absorption and low light yield of these perovskites restrict their practical applications. Quantum cutting can convert a high energy photon into multiple low energy photons, endowing a large Stokes shift and high photoluminescent quantum yield (PLQY). Here, this work reports a novel quantum cutting material, CsPbCl x Br 3−x :Yb 3+ perovskite SCs, with the PLQY of 149% and a Stokes shift >550 nm, successfully conquering the issues of poor PLQY induced by the thermal quenching and the large self-absorption in perovskite SCs. Benefiting from the extremely high PLQY and negligible self-absorption effect, the first high-performance quantum cutting scintillators based on CsPbCl x Br 3−x :Yb 3+ perovskite SCs are developed, exhibiting high transmittance, large X-ray absorption/conversion efficiency, outstanding light yield of ≈1.12 × 10 5 photons MeV −1 , and a detection limit as low as 176.5 nGy air s −1 . Finally, a single-pixel X-ray imaging is achieved by integrating CsPbCl 3 :Yb 3+ SCs with silicon photomultiplier. This work sheds light on exploring highly competitive scintillators beyond the scope of traditional perovskites.

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Penetration and Diffusion of X Rays

Cited by 85 publications

References 45 publications

Plural-series approximations of functions

Plural-series approximations of functions

Bounds to truncation errors in biorthogonal polynomial approximations, with illustrative applications to gamma ray transport distributions

X‐Ray Quantum Cutting Scintillator Based on CsPbCl_xBr₃₋_x:Yb³⁺ Single Crystals

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Penetration and Diffusion of X Rays

Cited by 85 publications

References 45 publications

Plural-series approximations of functions

Plural-series approximations of functions

Bounds to truncation errors in biorthogonal polynomial approximations, with illustrative applications to gamma ray transport distributions

X‐Ray Quantum Cutting Scintillator Based on CsPbClxBr3−x:Yb3+ Single Crystals

Contact Info

Product

Resources

About

X‐Ray Quantum Cutting Scintillator Based on CsPbCl_xBr₃₋_x:Yb³⁺ Single Crystals