{"title":"q-高斯Tsallis线形和拉曼光谱带","authors":"Amelia Carolina Sparavigna","doi":"10.18483/ijsci.2671","DOIUrl":null,"url":null,"abstract":"q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1<q<3, the q-functions pass from the usual Gaussian form, for q close to 1, to that of a heavy tailed distribution, at q close to 3. The value q=2 corresponds to the Cauchy-Lorentzian distribution. This behavior of q-Gaussian functions could be interesting for a specific application, that regarding the analysis of Raman spectra, where Lorentzian and Gaussian profiles are the line shapes most used to fit the spectral bands. Therefore, we will propose q-Gaussians with the aim of comparing the resulting fit analysis with data available in literature. As it will be clear from the discussion, this is a very sensitive issue. We will also provide a detailed discussion about Voigt and pseudo-Voigt functions and their role in the line shape modeling of Raman bands. We will show a successfully comparison of these functions with q-Gaussians. The role of q-Gaussians in EPR spectroscopy (Howarth et al., 2003), where the q-Gaussian is given as the ''Tsallis lineshape function'', will be reported. Two examples of fitting Raman D and G bands with q-Gaussians are proposed too.","PeriodicalId":14423,"journal":{"name":"International journal of sciences","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"q-Gaussian Tsallis Line Shapes and Raman Spectral Bands\",\"authors\":\"Amelia Carolina Sparavigna\",\"doi\":\"10.18483/ijsci.2671\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1<q<3, the q-functions pass from the usual Gaussian form, for q close to 1, to that of a heavy tailed distribution, at q close to 3. The value q=2 corresponds to the Cauchy-Lorentzian distribution. This behavior of q-Gaussian functions could be interesting for a specific application, that regarding the analysis of Raman spectra, where Lorentzian and Gaussian profiles are the line shapes most used to fit the spectral bands. Therefore, we will propose q-Gaussians with the aim of comparing the resulting fit analysis with data available in literature. As it will be clear from the discussion, this is a very sensitive issue. We will also provide a detailed discussion about Voigt and pseudo-Voigt functions and their role in the line shape modeling of Raman bands. We will show a successfully comparison of these functions with q-Gaussians. The role of q-Gaussians in EPR spectroscopy (Howarth et al., 2003), where the q-Gaussian is given as the ''Tsallis lineshape function'', will be reported. Two examples of fitting Raman D and G bands with q-Gaussians are proposed too.\",\"PeriodicalId\":14423,\"journal\":{\"name\":\"International journal of sciences\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18483/ijsci.2671\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18483/ijsci.2671","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
q-Gaussian Tsallis Line Shapes and Raman Spectral Bands
q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1
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