In addition to Chris's answer. I see the following article in Pubmed:
Di Saverio S, Gutierrez J, Avisar E. A retrospective review with long term follow up of 11,400 cases of pure mucinous breast carcinoma. Breast Cancer Res Treat. 2008 Oct;111(3):541-7. doi: https://doi.org/10.1007/s10549-007-9809-z. Epub 2007 Nov 18. PMID: 18026874.
This is a retrospective review, so not a clinical trial, but has follow-up data and data on the use and survival time with radiotherapy. It should be noted that it seems the gold standard procedure is lumpectomy (i.e. surgery to remove the cancer and sometimes associated lymph nodes), followed by adjuvant chemotherapy, usually platinum based (e.g. Cisplatin). Radiotherapy is also used as an adjuvant, not a primary treatment.
There's also this recent paper (2021), that covers mucinous ovarian carcinomas:
Craig O, Salazar C, Gorringe KL. Options for the Treatment of Mucinous Ovarian Carcinoma. Curr Treat Options Oncol. 2021 Nov 13;22(12):114. doi: https://doi.org/10.1007/s11864-021-00904-6. PMID: 34773517.
This one states (my emphasis):
Radiotherapy is not commonly used in modern MOC treatment. It may occasionally be used in the palliative setting for the purpose of symptom relief. Historically, radiotherapy was largely abandoned for the treatment of EOC with the advent and relative success of cisplatin chemotherapy. As most studies combined all EOC histotypes under one umbrella, this shift was driven primarily by data generated from HGSOC patients who comprised the vast majority of participants in such EOC trials. Since the widespread recognition of distinct EOC histotypes, there is limited data on the efficacy of radiotherapy in MOC patients. Some argue that within non-serous histotypes including mucinous, radiotherapy may have some merit and thus be worth revisiting in the curative setting . However, recent studies have presented conflicting findings regarding its benefit for the treatment of early-stage MOC [24, 25•, 26] (class III–IV), and thus, radiotherapy use generally remains limited and is not currently included in clinical guidelines for the treatment of MOC.
Refs 23-26 seem promising here:
23: Thomas G. Revisiting the role of radiation treatment for non-serous subtypes of epithelial ovarian cancer. Am Soc Clin Oncol Educ Book. 2013. doi:https://doi.org/10.1200/EdBook_AM.2013.33.e205.
24: Smart A, Chen YH, Cheng T, King M, Lee L. Salvage radiation therapy for localized recurrent ovarian cancer. Int J Gynecol Cancer. 2019. https://doi.org/10.1136/ijgc-2019-000247.
25: Kumar A, Le N, Gilks CB, Santos JL, Wong F, Swenerton K et al. Survival benefit of adjuvant radiotherapy: an analysis of low-stage invasive ovarian mucinous carcinomas. Int J Gynecol Cancer. 2017;27(9):1819-25. doi:https://doi.org/10.1097/igc.0000000000001124.
26: Patel SC, Frandsen J, Bhatia S, Gaffney D. Impact on survival with adjuvant radiotherapy for clear cell, mucinous, and endometriod ovarian cancer: the SEER experience from 2004 to 2011. J Gynecol Oncol. 2016;27(5): e45. https://doi.org/10.3802/jgo.2016.27.e45.
I am sure that a suitable search in PubMed would turn up many more articles.