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Polarisasi Spin Lambda 0 Pada Peluruhan Lambda 0 => P+Pi

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Polarisasi Spin Lambda 0 Pada Peluruhan Lambda 0 => P+Pi Penentuan Polarisasi Spin Λ0 pada Peluruhan Λ0 → p + π− JA Simanullang 0399020454 Universitas Indonesia Fakultas Matematika dan Ilmu Pengetahuan Alam Jurusan Fisika Depok Penentuan Polarisasi Spin Λ0 pada Peluruhan Λ0 → p + π− Skripsi Diajukan sebagai Salah Satu Syarat untuk Memperoleh Gelar Sarjana Sains JA Simanullang 0399020454 Depok 2003 Halaman Persetujuan Skripsi : Penentuan Polarisasi Spin Λ0 pada Peluruhan Λ0 → p + π− Nama : Jansen Agustinus Simanullang NPM : 0399020454 Skripsi ini telah diperiksa dan disetujui, Depok, ... Agustus 2003. Mengetahui, Dr T.Mart Pembimbing Dr. M. Hikam Penguji I Dr.L.T. Handoko Penguji II iii Kata Pengantar Skripsi ini merupakan persyaratan mendapatkan gelar S.Si, sarjana sains. Semoga karya yang pernah dikerjakan ini berguna. Saya mengucapkan terima kasih kepada Dr. T. Mart yang membimbing saya dalam pembuatan skripsi ini. Terima kasih kepada dewan penguji, Dr. M. Hikam dan Dr. L.T. Handoko. Penulis iv Intisari Abstrak Simetri paritas (P) dahulu dianggap kekal pada semua interaksi. Jika paritas kekal maka alam tidak memiliki preferensi arah. Ternyata alam tidak seperti demikian. Kekekalan paritas pada interaksi lemah ditumbangkan oleh T.D. Lee dan C.N Yang, serta Wu. Paritas tidak kekal pada semua interaksi lemah termasuk pada peluruhan Λ0 → p+π−. Jika paritas tidak kekal dalam peluruhan Λ, polarisasinya dapat diukur dengan menggunakan proses peluruhan Λ0 → p + π−. Kata kunci: peluruhan, polarisasi. Abstract Parity (P) symmetry was assumed to be conserved in all interactions. If parity were conserved then nature would not have any directional preference. Nature, however, is not so. Conservation of parity in weak interaction had been proven not always true by T.D Lee and C.N. Yang, with Wu. Parity is not conserved in all weak interactions including in the decay of Λ0 → p + π−. If parity were not conserved in decay of Λ, the polarization can be measured using the decay process of Λ0 → p+π−. Keywords: decay, polarization v Daftar Isi Halaman Persetujuan iii Kata Pengantar iv Intisari v Daftar Isi vii Daftar Gambar viii Daftar Tabel ix 1 Pendahuluan 1 1.1 Latar Belakang . 1 1.2 Metode Penelitian . 2 1.3 Tujuan Penelitian . 2 1.4 Sistematika Penulisan . 2 2 Tinjauan Pustaka 4 2.1 Tumbangnya Kekekalan Paritas . 4 2.2 Peluruhan Nonleptonik Hyperon . 5 3 Hasil dan Pembahasan 7 3.1 Amplitudo . 8 3.2 Kuadrat Amplitudo . 9 3.2.1 Kontribusi Gelombang-s ..................... 10 3.2.2 Kontribusi Gelombang-p ..................... 10 3.2.3 Suku Interferensi-sp ........................ 11 3.3 Polarisasi dan Laju Peluruhan . 12 3.4 Metode Pengkopelan Momentum Angular . 14 vi Daftar Isi Daftar Isi 4 Kesimpulan dan Saran 20 4.1 Kesimpulan . 20 4.2 Saran Penelitian ke Depan . 21 A Notasi Umum 22 A.1 Aljabar Dirac . 22 B Kopling Momentum Angular 25 C Parameter Peluruhan Baryon 27 C.1 Peluruhan Hyperon . 27 C.2 Sifat Peluruhan Hyperon . 30 Bibliografi 31 vii Daftar Gambar 3.1 Diagram Feynman Peluruhan Hyperon Nonleptonik . 8 3.2 Definisi sumbu dan arah pada peluruhan Λ . 15 3.3 Plot 1 − αP cos θ terhadap θ. ...................... 16 3.4 Distribusi angular proton peluruhan Λ dalam kerangka diam Λ . 18 viii Daftar Tabel 3.1 Hasil Perhitungan Data . 19 C.1 Sifat-sifat Peluruhan Hyperon . 30 ix Bab 1 Pendahuluan Manusia merupakan suatu keberadaan yang mempertanyakan keberadaan. Sejak zaman dahulu, manusia telah menyelidiki segala sesuatu baik yang ada maupun yang dianggap ada. Dalam penyelidikan itu manusia mencari simetri. Simetri merupakan suatu hal yang amat membantu dalam mempelajari segala sesuatu. Di dalam Fisika pun demikian. Para fisikawan mengejar simetri seba- gai suatu hal yang diidam-idamkan. Keberadaan simetri bisa membuat kagum para ilmuwan atas struktur alam semesta yang penuh misteri. Dari banyak simetri yang dikejar oleh para fisikawan terdapat tiga simetri diskret yang menggambarkan simetri partikel-antipartikel, simetri kiri-kanan, dan simetri maju-mundur. Ketiga simetri tersebut dikenal dengan nama konjugasi muatan, paritas dan pembalikan waktu. 1.1 Latar Belakang Eksperimen telah membuktikan bahwa simetri paritas tidak kekal pada semua in- teraksi. Pada interaksi lemah nyata-nyata hukum kekekalan paritas dilanggar. Se- andainya paritas kekal maka alam tidak akan memilih membedakan kiri dan kanan, alam tidak memiliki preferensi arah. Tetapi dalam interaksi lemah, alam tidak berlaku demikian. Alam betul-betul membedakan kiri dan kanan, dan memilih arah yang disukainya. Setelah eksperimen dari C.S. Wu memberikan bukti positif ketidakkekalan paritas, para fisikawan menyadari bahwa alam berlaku sedemikian sehingga dalam interaksi lemah alam mempunyai aturan yang berbeda untuk kiri 1 1.2. Metode Penelitian Bab 1. Pendahuluan dan kanan. Alam membedakan kiri dan kanan. Jika alam membedakan kiri dan kanan, akan terjadi berbagai hal yang menjadi konsekuensi pembedaan tersebut. Jika paritas tidak kekal, akan terjadi percampuran antara partikel yang memiliki paritas yang biasa dikenal dengan partikel serupa yang memiliki paritas yang berlawanan (yang tidak biasanya). Jika paritas tidak kekal, akan terjadi polarisasi spin yang menciptakan keberadaan momen dipol magnetik. Jika ketidakkekalan paritas ini terjadi dalam proses peluruhan hyperon, maka kedua konsekuensi ini memiliki makna bahwa polarisasi spin dapat dihitung melalui proses peluruhannya. 1.2 Metode Penelitian Penelitian ini bersifat teoretis, sehingga yang pertama diperlukan untuk menger- jakan penelitian ini adalah kerangka kerja teori yang memadai untuk dapat digu- nakan sebagai kerangka kerja kalkulasional. Kerangka kerja teori yang masih berlaku dan bekerja sampai saat ini adalah teori kuantum dan teori medan kuantum (Quan- tum Field Theory). Yang kedua yang diperlukan untuk mengerjakan penelitian ini adalah akses ke sumber informasi yang secara khusus berkaitan dengan tema peneli- tian. Sumber informasi yang dapat diakses dalam penelitian ini adalah buku teks dan jurnal. 1.3 Tujuan Penelitian Dalam penelitian ini ingin diperlihatkan bagaimana kaitan antara polarisasi spin Λ0 dengan proses peluruhannya, Λ0 → p + π−. Melalui penelitian ini, pembaca akan mendapati bahwa polarisasi Λ0 dapat dihitung dari laju peluruhannya. Hal ini dipakai oleh para eksperimentalis untuk mengukur polarisasi spin Λ0 tanpa meng- gunakan polarimeter. 1.4 Sistematika Penulisan Tulisan ini dibagi menjadi empat bab. Pembaca akan melihat tinjauan pustaka dalam Bab 2 yang akan memberikan gambaran perkembangan penelitian mengenai 2 1.4. Sistematika Penulisan Bab 1. Pendahuluan topik ketidakkekalan paritas dalam peluruhan hyperon. Tinjauan tersebut berisikan perkembangan pemikiran para fisikawan hingga mendapatkan kesimpulan bahwa ji- ka paritas tidak kekal maka polarisasi hyperon dapat diukur dengan menggunakan proses peluruhannya. Peninjauan hasil secara umum dalam penelitian ini dituliskan dalam Bab 3 yang akan memperlihatkan kaitan antara polarisasi spin dengan proses peluruhan. Selanjutnya, diperlihatkan metode perhitungan alternatif dalam kerang- ka kerja teoretis yang berbeda tetapi tetap menunjukkan pengaitan polarisasi dengan proses peluruhan. Terakhir, kelanjutan penelitian yang mungkin dilakukan di masa mendatang sekitar topik pelanggaran simetri pada peluruhan hyperon dipaparkan dalam Bab 4. Dalam bagian tersebut, ditegaskan bahwa penelitian ini hanya mem- pertimbangkan pelanggaran simetri paritas. Pelanggaran terhadap simetri gabun- gan antara konjugasi muatan dengan paritas belum dilakukan. Hal ini menjadi peluang untuk mengembangkan penelitian ini lebih lanjut ke dalam tema yang lebih luas. 3 Bab 2 Tinjauan Pustaka 2.1 Tumbangnya Kekekalan Paritas Dahulu orang menganggap bahwa paritas kekal pada semua interaksi, tetapi semua bukti eksperimental kekekalan paritas yang ada diperoleh dalam interaksi kuat dan elektromagnetik saja, dalam interaksi lemah belum ada bukti eksperimental. Per- tanyaan mengenai konservasi paritas dalam interaksi lemah dilontarkan pertama kali oleh Lee dan Yang [1]. Lee dan Yang menyarankan agar eksperimen dilakukan untuk mendapatkan bukti yang sahih atas kekekalan atau ketidakkekalan paritas. Berbagai eksperimen pun mulai dilakukan mengikuti saran Lee dan Yang. Lee dan Yang kemudian mengajukan pertanyaan lagi bersama dengan Oehme, kali ini mengenai invariansi mutlak terhadap konjugasi muatan karena bukti eksperimen- talnya pun belum ada [2]. Pada saat tulisan mereka dipublikasikan, ketidakkekalan paritas telah memperoleh bukti eksperimentalnya melalui eksperimen Co 60 yang dilakukan oleh Mme. CS Wu. Lee, Yang dan Wu mendapatkan penghargaan No- bel atas keberhasilan mereka menumbangkan kekekalan paritas. Paritas tidak kekal pada semua interaksi. Interaksi lemah tidak mengekalkan paritas. Tumbangnya kekekalan paritas memiliki banyak konsekuensi yang telah dipredik- si oleh Lee dan Yang. Apabila paritas tidak kekal pada interaksi lemah, maka par- itas hanya didefinisikan dan diukur pada interaksi kuat dan elektromagnetik saja. Jika paritas tidak kekal, semua keadaan atomik dan nuklir menjadi percampuran yang terdiri dari keadaan dengan paritas yang biasa dikenal bersama-sama dengan persentase kecil keadaan yang mempunyai paritas yang berlawanan. Ketidakkekalan 4 2.2. Peluruhan Nonleptonik Hyperon Bab 2. Tinjauan Pustaka paritas mengimplikasikan keberadaan interaksi yang mencampur paritas [1]. 2.2 Peluruhan Nonleptonik Hyperon Beberapa eksperimen lain semakin mengokohkan ketidakkekalan paritas. Peluruhan β, peluruhan π, dan peluruhan µ menyatakan ketidakkekalan paritas. Lee dan Yang kembali menginginkan klarifikasi ketidakkekalan paritas dalam
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